{"id":699,"date":"2023-08-12T09:22:00","date_gmt":"2023-08-12T03:52:00","guid":{"rendered":"https:\/\/iitmadrasstudentscommunity.me\/?p=699"},"modified":"2023-08-12T12:41:42","modified_gmt":"2023-08-12T07:11:42","slug":"statistics-week-9-graded-assignments-iit-madras","status":"publish","type":"post","link":"https:\/\/iitmadrasstudentscommunity.me\/statistics-week-9-graded-assignments-iit-madras\/","title":{"rendered":"Statistics Week 9 Graded Assignments IIT Madras"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"699\" class=\"elementor elementor-699\" 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-03ab778 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"03ab778\" 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-905dba2\" data-id=\"905dba2\" 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-3449234 elementor-widget elementor-widget-text-editor\" data-id=\"3449234\" 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<p><em>Statistics week 9 graded assignment Complete\u00a0 Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments Check Below For Master Key<\/em><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-011fd14 elementor-widget elementor-widget-text-editor\" data-id=\"011fd14\" 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; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"fET0JIgqzBRr\" class=\"qt-question-group\" 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; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div id=\"fET0JIgqzBRr.0.5340639134744576\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><p>1.A discrete random variable\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0can take the values 1,2,\u00b7\u00b7\u00b7,7. For these values the cumulative distribution function is defined by:<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)=\ufffd(\ufffd\u2264\ufffd)=\ufffd2+\ufffd95<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">F<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; 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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/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=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><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: 1.49111em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><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;\">95<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><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;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; text-align: left;\"><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=\"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 class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03148em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>;\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span>= 1,2,\u00b7\u00b7\u00b7,7. Find the value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03148em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">k<\/span><\/span><\/span><\/span><\/span>.<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\"><strong><span style=\"color: #0000ff;\">31<\/span><\/strong><\/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;\">\u00a0<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"UdNLiIrOLClJ\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"UdNLiIrOLClJ.0.6466982496960512\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>2.An organization in Texas organizes lucky draw this month. 3 thousand tickets are sold for 2$ each. Each has an equal chance of winning. 1 tickets will win 698$, 3 tickets will win 353$ and 4 tickets will win 63$. Let, the random variable\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0denote the net gain from purchase of one ticket. What is the probability that\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0takes the value less than 353? (Enter the answer correct to 4 decimal place)<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><strong><span style=\"color: #0000ff;\">0.9998<\/span><\/strong><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/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;\">\u00a0<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"DZAWueOpI9iM\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"DZAWueOpI9iM.0.5059607613407232\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>3. In a group of 204 people, 29 are photographers and 175 are journalists. 12 people are randomly picked from a group of these 204 people. Let,\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">Y<\/span><\/span><\/span><\/span><\/span>\u00a0be a random variable which represents the number of photographers. How many possible values can the random variable\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.22222em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">Y<\/span><\/span><\/span><\/span><\/span>\u00a0take?<\/p><div style=\"margin: 0px; padding: 0px;\"><span style=\"color: #0000ff;\"><strong>9<\/strong><\/span><\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/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;\">\u00a0<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"zyWM1JxcAQhk\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">4.<\/div><div id=\"zyWM1JxcAQhk.0.5911946188554240\" class=\"qt-mc-question qt-embedded\" 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;\">\u00a0<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">Which of the following is\/are discrete random variables?<\/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 id=\"zyWM1JxcAQhk.0.5911946188554240.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"zyWM1JxcAQhk.0.5911946188554240\" type=\"checkbox\" data-index=\"0\" \/><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.0\">Number of tires produced in an automotive tire factory every 30 minutes.<\/label><\/span><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"zyWM1JxcAQhk.0.5911946188554240.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"zyWM1JxcAQhk.0.5911946188554240\" type=\"checkbox\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.1\">The number of kernels(pieces) of popcorn in a\u00a0\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">1\ufffd\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03148em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">k<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">g<\/span><\/span><\/span><\/span><\/span>\u00a0container.<\/label><\/label><\/span><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"zyWM1JxcAQhk.0.5911946188554240.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"zyWM1JxcAQhk.0.5911946188554240\" type=\"checkbox\" data-index=\"2\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.2\">The time between customers entering a checkout lane at a retail store.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"zyWM1JxcAQhk.0.5911946188554240.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"zyWM1JxcAQhk.0.5911946188554240\" type=\"checkbox\" data-index=\"3\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.3\">The amount of rain recorded at an airport one day.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"zyWM1JxcAQhk.0.5911946188554240.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"zyWM1JxcAQhk.0.5911946188554240\" type=\"checkbox\" data-index=\"4\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.4\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.4\">The amount of liquid in a\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">2\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.01968em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">l<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">i<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">t<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">res<\/span><\/span><\/span><\/span><\/span>\u00a0bottle of soft drink.<\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"zyWM1JxcAQhk.0.5911946188554240.5\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"zyWM1JxcAQhk.0.5911946188554240\" type=\"checkbox\" data-index=\"5\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><span style=\"color: #0000ff;\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.5\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"zyWM1JxcAQhk.0.5911946188554240.5\">The number of no-shows for every\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">1000<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1000<\/span><\/span><\/span><\/span><\/span>\u00a0reservations made with a commercial airline.<\/label><\/label><\/span><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"sywHk7C3dmjZ\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"sywHk7C3dmjZ.0.6331971307307008\" class=\"qt-mc-question qt-embedded\" 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;\">\u00a0<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>5.A biased coin with probability of heads\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">0.75<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.75<\/span><\/span><\/span><\/span><\/span>\u00a0is tossed three times. Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0be a random variable that represents the number of head runs, a head run being defined as a consecutive occurrence of at least two heads. Then the probability mass function of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0is given by:<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/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;\"><p><input id=\"sywHk7C3dmjZ.0.6331971307307008.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"sywHk7C3dmjZ.0.6331971307307008\" type=\"radio\" data-index=\"0\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=\ufffd)={0.375for\u00a0\ufffd\u00a0=\u00a000.625for\u00a0\ufffd\u00a0=\u00a01<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; 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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"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; border-color: currentcolor; font-family: KaTeX_Size4;\">{<\/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=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.375<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><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;\">0.625<\/span><\/span><\/span><\/span><\/span><\/span><\/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=\"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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a00<\/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=\"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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a01<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"sywHk7C3dmjZ.0.6331971307307008.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"sywHk7C3dmjZ.0.6331971307307008\" type=\"radio\" data-index=\"1\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=\ufffd)={0.297for\u00a0\ufffd\u00a0=\u00a000.703for\u00a0\ufffd\u00a0=\u00a01<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; 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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"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; border-color: currentcolor; font-family: KaTeX_Size4;\">{<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; color: #0000ff;\"><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=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.297<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><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;\">0.703<\/span><\/span><\/span><\/span><\/span><\/span><\/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=\"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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a00<\/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=\"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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a01<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><p><input id=\"sywHk7C3dmjZ.0.6331971307307008.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"sywHk7C3dmjZ.0.6331971307307008\" type=\"radio\" data-index=\"2\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=\ufffd)={0.016for\u00a0\ufffd\u00a0=\u00a000.140for\u00a0\ufffd\u00a0=\u00a010.422for\u00a0\ufffd\u00a0=\u00a020.422for\u00a0\ufffd\u00a0=\u00a03<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; 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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" 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: 2.95002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.59999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.20002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/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: 3.13em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.13em;\"><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;\">0.016<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><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;\">0.140<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.25em;\"><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;\">0.422<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.81em;\"><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;\">0.422<\/span><\/span><\/span><\/span><\/span><\/span><\/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: 3.13em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -5.13em;\"><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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a00<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.69em;\"><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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a01<\/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=\"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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a02<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -0.81em;\"><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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a03<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><\/p><\/div><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/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;\"><p><input id=\"sywHk7C3dmjZ.0.6331971307307008.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"sywHk7C3dmjZ.0.6331971307307008\" type=\"radio\" data-index=\"3\" \/><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px; font-size: 16px;\" for=\"sywHk7C3dmjZ.0.6331971307307008.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=\ufffd)={0.016for\u00a0\ufffd\u00a0=\u00a000.844for\u00a0\ufffd\u00a0=\u00a010.140for\u00a0\ufffd\u00a0=\u00a02<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; 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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" 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: 2.35002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.19999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.60002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/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: 2.41em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.41em;\"><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;\">0.016<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.97em;\"><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;\">0.844<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53em;\"><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;\">0.140<\/span><\/span><\/span><\/span><\/span><\/span><\/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: 2.41em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.41em;\"><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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a00<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.97em;\"><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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a01<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53em;\"><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;\">for\u00a0<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00a0=\u00a02<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div>\u00a0<\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"HyOParcKOLfg\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"HyOParcKOLfg.0.6600664461344768\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>6. Nina has 6 music sessions in a week. She attends the sessions 6 days a week 59% of the time, 5 days 13% of the time, one day 7% of the time, and no days 21% of the time. Let,\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0be a discrete random variable representing the number of sessions she attends in a week. Suppose one week is randomly selected, what is the probability that the random variable\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0take the value at most 5?(Enter the answer correct to 2 decimal places)<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><strong><span style=\"color: #0000ff;\">Check Master Key Below<\/span><\/strong><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/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;\">\u00a0<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"5YRzxsXNL8Pn\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"5YRzxsXNL8Pn.0.5411366777126912\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>7.Find the value of k for which k<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">(47)\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><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 size3\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size3;\">(<\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><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=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">7<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><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><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; top: 0em;\"><span class=\"delimsizing size3\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size3;\">)<\/span><\/span><\/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: 1.50429em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.9029em;\"><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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>( x = 0, 1, 2, &#8230;) is a pmf.(Enter the answer correct up to 2 decimal places)<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><strong><span style=\"color: #0000ff;\">0.625<\/span><\/strong><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/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;\">\u00a0<\/em><\/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; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"5YRzxsXNL8Pn.1.5415054677639168\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>8.Using the information in previous question, calculate\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=2)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; 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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>.(Enter the answer correct up to 2 decimal places)<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><span style=\"color: #0000ff;\"><strong>0.09<\/strong><\/span><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/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;\">\u00a0<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"l2eV72CjBPYg\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"l2eV72CjBPYg.0.4906752042598400\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>9.From a box\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><\/span><\/span><\/span><\/span>\u00a0containing 3 white and 6 black balls, 5 balls are transferred into an empty box\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><\/span><\/span><\/span><\/span>. Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0be a random variable that represents the number of white balls which are transferred from\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">A<\/span><\/span><\/span><\/span><\/span>\u00a0to\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">B<\/span><\/span><\/span><\/span><\/span>. What value of random variable will have the least probability?<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><strong>0<\/strong><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/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;\">\u00a0<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-family: Roboto, 'Helvetica Neue', sans-serif; font-size: 14px; background-color: #fafafc;\"><div id=\"X3iZkXmUKdzT\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; background-color: #ffffff; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"X3iZkXmUKdzT.0.4812532715880448\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><p>10. The probability mass function of a random variable X is given by:<\/p><\/div><div>\u00a0<\/div><div>\u00a0<\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><p><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0 \u00a0 \u00a0 \u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; 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; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/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=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>=\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">{3\ufffd2\u22123\ufffdfor\u00a0\ufffd=02\ufffd2\u22121for\ufffd=10otherwise<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"minner\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"delimsizing mult\" 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: 2.35002em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.19999em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a9<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.15001em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a8<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.60002em;\"><span class=\"delimsizinginner delim-size4\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Size4;\">\u23a7<\/span><\/span><\/span><\/span><\/span><\/span><\/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: 2.41em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.41em;\"><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 class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03148em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">k<\/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=\"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 class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03148em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">k<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.97em;\"><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;\">2<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03148em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">k<\/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=\"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 class=\"mbin\" 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 class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -1.53em;\"><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;\">0<\/span><\/span><\/span><\/span><\/span><\/span><\/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: 2.41em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -4.41em;\"><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;\">for\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.97em;\"><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;\">for<\/span><\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">x<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><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: -1.53em;\"><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;\">otherwise<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br style=\"margin: 0px; padding: 0px;\" \/><br style=\"margin: 0px; padding: 0px;\" \/>\u00a0Determine the value of k given\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; text-rendering: auto; 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, 'Times New Roman', serif;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd&gt;0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.03148em 0px 0px; padding: 0px; border-color: currentcolor; font-family: KaTeX_Math; font-style: italic;\">k<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/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=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>.<\/p><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><strong><span style=\"color: #0000ff;\">1<\/span><\/strong><\/div><\/div><\/div><\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4c79324 elementor-widget elementor-widget-text-editor\" data-id=\"4c79324\" 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<h3><strong><a href=\"https:\/\/iitmadrasstudentscommunity.me\/wp-content\/uploads\/2023\/08\/week-9-stats-Graded-Assignments.pdf\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Week 9 Graded Assignments IIT Madras<\/a> \u00a0<\/strong><\/h3>\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-329b040 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"329b040\" 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-1b04f85\" data-id=\"1b04f85\" 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-4d7862f\" data-id=\"4d7862f\" 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-cd7a015 elementor-button-success elementor-align-center elementor-widget elementor-widget-button\" data-id=\"cd7a015\" 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 9 graded assignment Complete\u00a0 Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments Check Below For Master Key 1.A discrete random variable\u00a0\ufffdX\u00a0can take the values 1,2,\u00b7\u00b7\u00b7,7. For these values the cumulative distribution function is&hellip;&nbsp;<a href=\"https:\/\/iitmadrasstudentscommunity.me\/statistics-week-9-graded-assignments-iit-madras\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Statistics Week 9 Graded Assignments IIT Madras<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":747,"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":[56,68,70,69,67,71,20],"_links":{"self":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/699"}],"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=699"}],"version-history":[{"count":11,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/699\/revisions"}],"predecessor-version":[{"id":951,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/699\/revisions\/951"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media\/747"}],"wp:attachment":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media?parent=699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/categories?post=699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/tags?post=699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}