{"id":739,"date":"2023-08-12T09:52:00","date_gmt":"2023-08-12T04:22:00","guid":{"rendered":"https:\/\/iitmadrasstudentscommunity.me\/?p=739"},"modified":"2023-08-12T09:54:25","modified_gmt":"2023-08-12T04:24:25","slug":"statistics-week-10-graded-assignments","status":"publish","type":"post","link":"https:\/\/iitmadrasstudentscommunity.me\/statistics-week-10-graded-assignments\/","title":{"rendered":"Statistics Week 10 Graded Assignments"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"739\" class=\"elementor elementor-739\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-602f82f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"602f82f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-05ae6fb\" data-id=\"05ae6fb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-069d43e elementor-widget elementor-widget-text-editor\" data-id=\"069d43e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<div class=\"elementor-element elementor-element-08ded6a elementor-widget elementor-widget-text-editor\" data-id=\"08ded6a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\"><div class=\"elementor-widget-container\"><p><em>Statistics Week 10 graded assignment Complete\u00a0 Solutions Key Given In This Page Check Below . We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons If Not Able To Complete Graded Assignments\u00a0<\/em><\/p><\/div><\/div><div class=\"elementor-element elementor-element-ed2c490 elementor-widget elementor-widget-text-editor\" data-id=\"ed2c490\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\"><div class=\"elementor-widget-container\">\u00a0<\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-649a492 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"649a492\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9c1123f\" data-id=\"9c1123f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3d2b7e5 elementor-widget elementor-widget-text-editor\" data-id=\"3d2b7e5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"qt-question-group\" id=\"EEMzHZtWnfXB\" style=\"margin: 0px; padding: 0px;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"qt-sa-question qt-embedded\" id=\"EEMzHZtWnfXB.0.6113493468053504\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">There are&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mn>6<\/mn><\/msup><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.814108em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>numbered cards in a deck among which&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><\/mrow><mn>6<\/mn><\/msup><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.964108em; vertical-align: -0.15em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;cards bear the number&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo separator=\"true\">;<\/mo><mi>\ufffd<\/mi><mo>=<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mi mathvariant=\"normal\">.<\/mi><mi mathvariant=\"normal\">.<\/mi><mi mathvariant=\"normal\">.<\/mi><mo separator=\"true\">,<\/mo><mn>6<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">;<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.83888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&#8230;<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><\/span><\/span>. From the deck, 10 cards are drawn with replacement. What is the expectation of the sum of their numbers?(Enter the answer correct to 1 decimal accuracy)<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-EEMzHZtWnfXB.0.6113493468053504\" step=\"any\" type=\"number\" fdprocessedid=\"9ntvjq\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: rgb(5, 166, 96);\"><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"qt-question-group\" id=\"8USNuvRXhztQ\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\"><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-mc-question qt-embedded\" id=\"8USNuvRXhztQ.0.5686107412889600\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div>An unbiased die is thrown 13 times. After each throw a &#8216;+&#8217; is recorded for 2 or 5 and &#8216;-&#8216; is recorded for 1,3,4 or 6, the signs forming an ordered sequence. To each, except the first and last sign, a random variable&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><mo separator=\"true\">;<\/mo><mi>\ufffd<\/mi><mo>=<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mi mathvariant=\"normal\">.<\/mi><mi mathvariant=\"normal\">.<\/mi><mi mathvariant=\"normal\">.<\/mi><mo separator=\"true\">,<\/mo><mn>11<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">;<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.83888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&#8230;<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">11<\/span><\/span><\/span><\/span><\/span>&nbsp;is associated which takes the value&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>&nbsp;if both of its neighbouring sign differs from the one between them and&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>&nbsp;otherwise. If the random variable&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><\/span><\/span><\/span><\/span>&nbsp;is defined as&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo>=<\/mo><mn>3<\/mn><mi>\ufffd<\/mi><mo>+<\/mo><mn>13<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.76666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">13<\/span><\/span><\/span><\/span><\/span>&nbsp;where,&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo>=<\/mo><msubsup><mo>\u2211<\/mo><mrow><mi>\ufffd<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mn>11<\/mn><\/msubsup><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1.25372em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop op-symbol small-op\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size1; border-color: currentcolor; position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.954008em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.40029em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mrel mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.2029em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">11<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.29971em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<br style=\"margin: 0px; padding: 0px;\">Find the expected value of&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><\/span><\/span><\/span><\/span>.<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"0\" id=\"8USNuvRXhztQ.0.5686107412889600.0\" name=\"8USNuvRXhztQ.0.5686107412889600\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"8USNuvRXhztQ.0.5686107412889600.0\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>183<\/mn><mn>9<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 32.3125px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">183<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"1\" id=\"8USNuvRXhztQ.0.5686107412889600.1\" name=\"8USNuvRXhztQ.0.5686107412889600\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"8USNuvRXhztQ.0.5686107412889600.1\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>139<\/mn><mn>9<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 32.3125px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">139<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"2\" id=\"8USNuvRXhztQ.0.5686107412889600.2\" name=\"8USNuvRXhztQ.0.5686107412889600\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"8USNuvRXhztQ.0.5686107412889600.2\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>22<\/mn><mn>9<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 21.5375px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"3\" id=\"8USNuvRXhztQ.0.5686107412889600.3\" name=\"8USNuvRXhztQ.0.5686107412889600\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"8USNuvRXhztQ.0.5686107412889600.3\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>66<\/mn><mn>9<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 21.5375px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">66<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-mc-question qt-embedded\" id=\"8USNuvRXhztQ.1.5458293992456192\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div>An unbiased die is thrown 13 times. After each throw a &#8216;+&#8217; is recorded for 2 or 5 and &#8216;-&#8216; is recorded for 1,3,4 or 6, the signs forming an ordered sequence. To each, except the first and last sign, a random variable&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><mo separator=\"true\">;<\/mo><mi>\ufffd<\/mi><mo>=<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mi mathvariant=\"normal\">.<\/mi><mi mathvariant=\"normal\">.<\/mi><mi mathvariant=\"normal\">.<\/mi><mo separator=\"true\">,<\/mo><mn>11<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">;<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.83888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&#8230;<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">11<\/span><\/span><\/span><\/span><\/span>&nbsp;is associated which takes the value&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>&nbsp;if both of its neighbouring sign differs from the one between them and&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>&nbsp;otherwise. If the random variable&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><\/span><\/span><\/span><\/span>&nbsp;is defined as&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo>=<\/mo><mn>3<\/mn><mi>\ufffd<\/mi><mo>+<\/mo><mn>13<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.76666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">13<\/span><\/span><\/span><\/span><\/span>&nbsp;where,&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo>=<\/mo><msubsup><mo>\u2211<\/mo><mrow><mi>\ufffd<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mn>11<\/mn><\/msubsup><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1.25372em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop op-symbol small-op\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size1; border-color: currentcolor; position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.954008em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.40029em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mrel mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.2029em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">11<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.29971em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin: 0px 0.166667em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<br style=\"margin: 0px; padding: 0px;\">Which of the following statement(s) is\/are true?<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"0\" id=\"8USNuvRXhztQ.1.5458293992456192.0\" name=\"8USNuvRXhztQ.1.5458293992456192\" type=\"checkbox\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\"><label for=\"8USNuvRXhztQ.1.5458293992456192.0\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>3<\/mn><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>13<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">13<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"1\" id=\"8USNuvRXhztQ.1.5458293992456192.1\" name=\"8USNuvRXhztQ.1.5458293992456192\" type=\"checkbox\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\"><label for=\"8USNuvRXhztQ.1.5458293992456192.1\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>9<\/mn><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">V<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">V<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"2\" id=\"8USNuvRXhztQ.1.5458293992456192.2\" name=\"8USNuvRXhztQ.1.5458293992456192\" type=\"checkbox\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\"><label for=\"8USNuvRXhztQ.1.5458293992456192.2\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>9<\/mn><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>13<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">13<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"3\" id=\"8USNuvRXhztQ.1.5458293992456192.3\" name=\"8USNuvRXhztQ.1.5458293992456192\" type=\"checkbox\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\"><label for=\"8USNuvRXhztQ.1.5458293992456192.3\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>9<\/mn><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>13<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">V<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">V<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">13<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"qt-question-group\" id=\"13Sgvh9bLTBa\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\"><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-mc-question qt-embedded\" id=\"13Sgvh9bLTBa.0.6035249901338624\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div>Amandeep is in the middle of a bridge of infinite length. He takes the unit step to the right with probability 0.66 and to the left with probability 0.34. Assume that the movements are independent of each other.<br style=\"margin: 0px; padding: 0px;\"><span style=\"margin: 0px; padding: 0px; font-weight: bolder;\">Hint:<\/span>&nbsp;Consider the random variable&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;associated with the&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>\ufffd<\/mi><mrow><mi>\ufffd<\/mi><mi>\u210e<\/mi><\/mrow><\/msup><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.849108em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.849108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">t<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">h<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;step defined as:<br style=\"margin: 0px; padding: 0px;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.3600em\" columnalign=\"left left\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>1<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mtext>if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;right&nbsp;<\/mtext><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mtext>if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;left&nbsp;<\/mtext><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 3.00003em; vertical-align: -1.25003em;\"><\/span><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen delimcenter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; top: 0em;\"><span class=\"delimsizing size4\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size4; border-color: currentcolor;\">{<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.19em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 1em;\"><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;right&nbsp;<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;left&nbsp;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.19em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\">What is the expected distance between the starting point and end point of Amandeep after 5 steps?<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"0\" id=\"13Sgvh9bLTBa.0.6035249901338624.0\" name=\"13Sgvh9bLTBa.0.6035249901338624\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.0.6035249901338624.0\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>\u2212<\/mo><mn>0.32<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.32<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"1\" id=\"13Sgvh9bLTBa.0.6035249901338624.1\" name=\"13Sgvh9bLTBa.0.6035249901338624\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.0.6035249901338624.1\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1.6<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1.6<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"2\" id=\"13Sgvh9bLTBa.0.6035249901338624.2\" name=\"13Sgvh9bLTBa.0.6035249901338624\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.0.6035249901338624.2\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>\u2212<\/mo><mn>1.6<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1.6<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"3\" id=\"13Sgvh9bLTBa.0.6035249901338624.3\" name=\"13Sgvh9bLTBa.0.6035249901338624\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.0.6035249901338624.3\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0.32<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.32<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-mc-question qt-embedded\" id=\"13Sgvh9bLTBa.1.5306312212611072\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div>Amandeep is in the middle of a bridge of infinite length. He takes the unit step to the right with probability 0.66 and to the left with probability 0.34. Assume that the movements are independent of each other.<br style=\"margin: 0px; padding: 0px;\"><span style=\"margin: 0px; padding: 0px; font-weight: bolder;\">Hint:<\/span>&nbsp;Consider the random variable&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;associated with the&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>\ufffd<\/mi><mrow><mi>\ufffd<\/mi><mi>\u210e<\/mi><\/mrow><\/msup><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.849108em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.849108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">t<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">h<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;step defined as:<br style=\"margin: 0px; padding: 0px;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\ufffd<\/mi><mi>\ufffd<\/mi><\/msub><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07847em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.15em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.3600em\" columnalign=\"left left\" columnspacing=\"1em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mn>1<\/mn><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mtext>if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;right&nbsp;<\/mtext><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mtext>if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;left&nbsp;<\/mtext><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 3.00003em; vertical-align: -1.25003em;\"><\/span><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen delimcenter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; top: 0em;\"><span class=\"delimsizing size4\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size4; border-color: currentcolor;\">{<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mtable\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.19em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 1em;\"><\/span><span class=\"col-align-l\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.69em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;right&nbsp;<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3.008em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord text\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">if&nbsp;the&nbsp;step&nbsp;of&nbsp;Amandeep&nbsp;is&nbsp;towards&nbsp;the&nbsp;left&nbsp;<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.19em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\">What is the variance distance between the starting point and end point of Amandeep after 5 steps?<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"0\" id=\"13Sgvh9bLTBa.1.5306312212611072.0\" name=\"13Sgvh9bLTBa.1.5306312212611072\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.1.5306312212611072.0\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>4.49<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4.49<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"1\" id=\"13Sgvh9bLTBa.1.5306312212611072.1\" name=\"13Sgvh9bLTBa.1.5306312212611072\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.1.5306312212611072.1\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0.9<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.9<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"2\" id=\"13Sgvh9bLTBa.1.5306312212611072.2\" name=\"13Sgvh9bLTBa.1.5306312212611072\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.1.5306312212611072.2\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1.56<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1.56<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"3\" id=\"13Sgvh9bLTBa.1.5306312212611072.3\" name=\"13Sgvh9bLTBa.1.5306312212611072\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"13Sgvh9bLTBa.1.5306312212611072.3\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"qt-question-group\" id=\"eeEgJQ6dmG1n\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\"><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-sa-question qt-embedded\" id=\"eeEgJQ6dmG1n.0.6409362088132608\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">A box contains 10 white and 6 black balls. 2 balls are drawn at random without replacement. Find the expected value of the number of white balls drawn. (Enter the answer correct to 2 decimal places)<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-eeEgJQ6dmG1n.0.6409362088132608\" step=\"any\" type=\"number\" fdprocessedid=\"ythphf\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: rgb(5, 166, 96);\"><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-mc-question qt-standalone\" id=\"KMYyVMOdPJlv\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div>Rohit wants to open his door with&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span>&nbsp;keys(out of which&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>&nbsp;will open the door) and tries the keys independently and at random. If unsuccessful keys are eliminated from further selection, then Find the expected number of trials required to open the door.<br style=\"margin: 0px; padding: 0px;\"><span style=\"margin: 0px; padding: 0px; font-weight: bolder;\">Hint<\/span>: Suppose Rohit gets the first success at&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>\ufffd<\/mi><mrow><mi>\ufffd<\/mi><mi>\u210e<\/mi><\/mrow><\/msup><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.849108em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.849108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">t<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">h<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;trial, i.e., he is unable to open the door in the first&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">x<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>&nbsp;trials.<br style=\"margin: 0px; padding: 0px;\">And, P(he gets first success at second trial)=<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><\/mstyle><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 9.425px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 9.425px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"0\" id=\"KMYyVMOdPJlv.0\" name=\"KMYyVMOdPJlv\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"KMYyVMOdPJlv.0\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\">1<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"1\" id=\"KMYyVMOdPJlv.1\" name=\"KMYyVMOdPJlv\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"KMYyVMOdPJlv.1\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\">9<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"2\" id=\"KMYyVMOdPJlv.2\" name=\"KMYyVMOdPJlv\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"KMYyVMOdPJlv.2\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\">3<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"3\" id=\"KMYyVMOdPJlv.3\" name=\"KMYyVMOdPJlv\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"KMYyVMOdPJlv.3\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\">2<\/label><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"qt-question-group\" id=\"TOixogaau7fm\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\"><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-sa-question qt-embedded\" id=\"TOixogaau7fm.0.5690635281498112\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>&nbsp;and&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><\/span><\/span><\/span><\/span>&nbsp;are independent random variables with means 14 and 20, and variances 2 and 6 respectively. Find the variance of&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>\ufffd<\/mi><mo>+<\/mo><mn>6<\/mn><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.76666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><\/span><\/span><\/span><\/span>.<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-TOixogaau7fm.0.5690635281498112\" step=\"any\" type=\"number\" fdprocessedid=\"mc4zci\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: rgb(5, 166, 96);\"><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"qt-question-group\" id=\"AbSLRoBv8RPU\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\"><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-sa-question qt-embedded\" id=\"AbSLRoBv8RPU.0.4723045453266944\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div>Table Q10.1.G. represents the probability mass function of a random variable X<center style=\"margin: 0px; padding: 0px;\"><table class=\"content-table\" style=\"margin-top: 25px; margin-bottom: 25px; padding: 0px; caption-side: bottom; border-collapse: collapse; font-size: 0.9em; min-width: 400px; border-radius: 5px 5px 0px 0px; overflow: hidden; box-shadow: rgba(0, 0, 0, 0.15) 0px 0px 20px;\"><thead style=\"margin: 0px; padding: 0px; border-width: 0px; border-image: initial;\"><tr style=\"margin: 0px; padding: 0px; border-width: 0px; border-image: initial; background-color: rgb(0, 152, 121); color: rgb(255, 255, 255); font-weight: bold;\"><th style=\"margin: 0px; padding: 12px 15px; text-align: center; border-color: inherit; border-width: 0px; border-image: initial;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span><\/th><th style=\"margin: 0px; padding: 12px 15px; text-align: center; border-color: inherit; border-width: 0px; border-image: initial;\">-1<\/th><th style=\"margin: 0px; padding: 12px 15px; text-align: center; border-color: inherit; border-width: 0px; border-image: initial;\">4<\/th><th style=\"margin: 0px; padding: 12px 15px; text-align: center; border-color: inherit; border-width: 0px; border-image: initial;\">5<\/th><\/tr><\/thead><tbody style=\"margin: 0px; padding: 0px; border-width: 0px; border-image: initial;\"><tr style=\"margin: 0px; padding: 0px; border-width: 0px 0px 2px; border-bottom-style: solid; border-bottom-color: rgb(0, 152, 121); border-image: initial;\"><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo>=<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">P<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">6<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 8.4875px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 8.4875px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>9<\/mn><mn>18<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">18<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 16.9625px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">9<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><\/tbody><caption align=\"bottom\" style=\"margin: 0px; padding: 0.5rem 0px; color: rgb(108, 117, 125); text-align: left;\">Table Q10.1.G: Probability Mass Function<\/caption><\/table><\/center>Calculate the value of&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>\ufffd<\/mi><mo>+<\/mo><mn>1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1.06411em; vertical-align: -0.25em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. (Enter the answer correct to 2 decimal places)<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-AbSLRoBv8RPU.0.4723045453266944\" step=\"any\" type=\"number\" fdprocessedid=\"kxm9f\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: rgb(5, 166, 96);\"><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" role=\"alert\" style=\"margin: 0px; padding: 0px;\"><\/div><\/div><\/div><p><br style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"qt-question-group\" id=\"dD3WMPllyUiQ\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\"><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: rgb(225, 225, 225) 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\"><\/div><div class=\"qt-mc-question qt-embedded\" id=\"dD3WMPllyUiQ.0.6670223771959296\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div>Suppose that&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>&nbsp;is a random variable for which&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>15<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">15<\/span><\/span><\/span><\/span><\/span>&nbsp;and&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mi>\ufffd<\/mi><mi>\ufffd<\/mi><mo stretchy=\"false\">(<\/mo><mi>\ufffd<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>22<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Va<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">r<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><\/span><\/span>. Find the positive values of&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">a<\/span><\/span><\/span><\/span><\/span>&nbsp;and&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">b<\/span><\/span><\/span><\/span><\/span>&nbsp;such that&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\ufffd<\/mi><mo>=<\/mo><mi>\ufffd<\/mi><mi>\ufffd<\/mi><mo>\u2212<\/mo><mi>\ufffd<\/mi><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Y<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mspace\" style=\"margin: 0px 0.277778em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.76666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">a<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mspace\" style=\"margin: 0px 0.222222em 0px 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">b<\/span><\/span><\/span><\/span><\/span>, has expectation&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>&nbsp;and variance&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>.<div style=\"margin: 0px; padding: 0px;\"><\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"0\" id=\"dD3WMPllyUiQ.0.6670223771959296.0\" name=\"dD3WMPllyUiQ.0.6670223771959296\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"dD3WMPllyUiQ.0.6670223771959296.0\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><msqrt><mn>22<\/mn><\/msqrt><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.25144em; vertical-align: -0.93em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.20278em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.90722em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.86722em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"hide-tail\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; overflow: hidden; position: relative; width: 37.6625px; display: inline-block; min-width: 0.853em; height: 1.08em;\"><svg width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"><\/path><\/svg><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.13278em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 37.6625px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.93em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;,&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mo>\u2212<\/mo><mn>15<\/mn><\/mrow><msqrt><mn>22<\/mn><\/msqrt><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.25144em; vertical-align: -0.93em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.20278em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.90722em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.86722em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"hide-tail\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; overflow: hidden; position: relative; width: 37.6625px; display: inline-block; min-width: 0.853em; height: 1.08em;\"><svg width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"><\/path><\/svg><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.13278em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 37.6625px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">15<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.93em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"1\" id=\"dD3WMPllyUiQ.0.6670223771959296.1\" name=\"dD3WMPllyUiQ.0.6670223771959296\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"dD3WMPllyUiQ.0.6670223771959296.1\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>&nbsp;,&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>15<\/mn><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">15<\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"2\" id=\"dD3WMPllyUiQ.0.6670223771959296.2\" name=\"dD3WMPllyUiQ.0.6670223771959296\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"dD3WMPllyUiQ.0.6670223771959296.2\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mn>22<\/mn><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.00744em; vertical-align: -0.686em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 21.5375px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.686em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;,&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>15<\/mn><msqrt><mn>22<\/mn><\/msqrt><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.25144em; vertical-align: -0.93em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.20278em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.90722em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.86722em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"hide-tail\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; overflow: hidden; position: relative; width: 37.6625px; display: inline-block; min-width: 0.853em; height: 1.08em;\"><svg width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"><\/path><\/svg><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.13278em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 37.6625px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">15<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.93em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\"><\/div><\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input data-index=\"3\" id=\"dD3WMPllyUiQ.0.6670223771959296.3\" name=\"dD3WMPllyUiQ.0.6670223771959296\" type=\"radio\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: rgb(5, 166, 96);\"><label for=\"dD3WMPllyUiQ.0.6670223771959296.3\" style=\"margin: 0px 0px 0px 16px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\"><\/div><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><msqrt><mn>22<\/mn><\/msqrt><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.25144em; vertical-align: -0.93em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.20278em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.90722em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.86722em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"hide-tail\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; overflow: hidden; position: relative; width: 37.6625px; display: inline-block; min-width: 0.853em; height: 1.08em;\"><svg width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"><\/path><\/svg><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.13278em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 37.6625px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.93em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp;,&nbsp;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, &quot;Times New Roman&quot;, serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mn>15<\/mn><msqrt><mn>22<\/mn><\/msqrt><\/mfrac><\/mstyle><\/mrow><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"strut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; height: 2.25144em; vertical-align: -0.93em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen nulldelimiter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 0.12em;\"><\/span><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center; color: rgba(0, 0, 0, 0.87);\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.20278em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord sqrt\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.90722em;\"><span class=\"svg-align\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left; display: block; height: 0px; position: relative; top: -3em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px 0px 0px 0.833em; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">22<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.86722em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"hide-tail\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; overflow: hidden; position: relative; width: 37.6625px; display: inline-block; min-width: 0.853em; height: 1.08em;\"><svg width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"><\/path><\/svg><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.13278em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative;\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.23em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"frac-line\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; width: 37.6625px; min-height: 1px; border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"pstrut\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; overflow: hidden; width: 0px; height: 3em;\"><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">15<\/span><\/span><\/span><\/span><span class=\"vlist-s\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; font-size: 1px; min-width: 2px; vertical-align: bottom; width: 2px;\"><br><br><\/span><\/span><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center; color: rgba(0, 0, 0, 0.87);\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/div><\/div><\/div><\/div><\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-53de4b8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"53de4b8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-b8e09a7\" data-id=\"b8e09a7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-22f8a69\" data-id=\"22f8a69\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-523f734 elementor-button-success elementor-align-center elementor-widget elementor-widget-button\" data-id=\"523f734\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/drive.google.com\/drive\/folders\/15whlEXcbyshK1UjEZ3Uvdqt4tUa8YTXe?usp=sharing\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Access Master Key <\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Statistics Week 10 graded assignment Complete\u00a0 Solutions Key Given In This Page Check Below . We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons If Not Able To Complete Graded Assignments\u00a0 There are&nbsp; 2626numbered cards in a deck among which&nbsp; 6\ufffd\ufffd6Ci&nbsp;cards bear the number&nbsp; \ufffd;\ufffd=0,1,2,&#8230;,6i;i=0,1,2,&#8230;,6. From the deck,&hellip;&nbsp;<a href=\"https:\/\/iitmadrasstudentscommunity.me\/statistics-week-10-graded-assignments\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Statistics Week 10 Graded Assignments<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":780,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","neve_meta_reading_time":"","_themeisle_gutenberg_block_has_review":false,"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"categories":[10],"tags":[56,78,69,21],"_links":{"self":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/739"}],"collection":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/comments?post=739"}],"version-history":[{"count":8,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/739\/revisions"}],"predecessor-version":[{"id":924,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/739\/revisions\/924"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media\/780"}],"wp:attachment":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media?parent=739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/categories?post=739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/tags?post=739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}