Week 11 Graded Assignments – Students Community

Statistics Week 11 Graded Assignments IIT Madras

Khushi Dii — Tue, 15 Aug 2023 14:39:08 +0000

Statistics week 11 graded assignment Complete 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

A match predictor claims that he can predict the result of a match correctly 77% of the time. It is agreed that his claim will be accepted if he correctly predicts the results of at least 4 of 8 matches. What is the probability that his claim gets rejected?

\sum_{i = 1}^{3}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

\sum_{i = 0}^{3}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

\sum_{i = 0}^{4}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

\sum_{i = 1}^{4}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

1 point

X \sim B in o mia l (n, p)

, then which of the following statement/s is/are always true? (

n > 0

and

0 < p < 1

)

E (X) \leq Va r (X)

E (X) < Va r (X)

E (X) \geq Va r (X)

E (X) > Va r (X)

Va r (X) \leq S . D (X)

Va r (X) \geq S . D (X)

Two friends (say ‘

A

‘ and ‘

B

‘) could not decide whether to play a racing game or a boxing game on Xbox. They decide to play a card-game first. If ‘

A

‘ wins at least 3 rounds out of the 5 rounds of the card game played, then the boxing game will be played. The chances of ‘

A

‘ winning in any round of the card game is 2:5. Find the probability that the boxing game will be played on Xbox? (Enter the answer correct to 2 decimal places)
Hint: If the chances of happening of an event is x:y then, the probability equals

x + y x

1 point

Let

X

~ Binomial(6,p). If the probabilities of 4 and 5 successes are approximately 0.311 and, 0.1866 respectively, then find the parameter ‘p’ of the distribution.(Enter the answer correct to 2 decimal places)

1 point

If the expected number of sixes hit by a batsman on

n

balls is 6.39 and the variance for the same is 1.8531, then what is the probability of him hitting at least one six on any randomly selected

n

balls? Assume that the probability of him hitting a six on any ball is constant. (Enter the answer correct to 4 decimal places)

1 point

The probability of a student clearing a competitive exam is

4 1

. If he gives the exam 6 times, then what is the probability of him clearing the exam at least twice?(Enter the answer correct to 2 decimal places)

1 point

Choose the correct condition/s about binomial distribution.

The probability of success

p

keeps varying for each trial.

The number of trials

n

is finite.

The trials are dependent on each other.

The trials are independent of each other.

Rithika wants to test whether the coin she has is a fair coin or not. To test this, she conducted an experiment of tossing the coin 5 times. Binomial random variable

X

is defined as the total number of heads(

i

) after 5 tosses. The probability distribution of the binomial random variable is given in Table 11.1.G.

Table 11.1.G: Binomial Distribution
$X = i$	$P (X = i)$
0	0.00032
1	0.0064
2	0.0512
3	0.2048
4	0.4096
5	0.32768

What is the approximate probability of getting a head in tossing the given coin? (Enter the answer correct to one decimal place)

1 point

At a school function, It is noticed that 9% of the students are not wearing polished shoes and 12% of students are not wearing school ties. It is announced that the students who have committed any of the infractions will be punished, and that these two infractions are independent of one another. If a teacher selects 5 students at random, then find the probability that exactly three of the students will be punished for any of the infractions?

^{5} C_{3} (0.1992)^{3} (0.8008)^{2}

^{5} C_{3} (0.0108)^{3} (0.9892)^{2}

^{5} C_{3} (0.09)^{3} (0.91)^{2} +^{5} C_{3} (0.12)^{3} (0.88)^{2}

^{5} C_{3} (0.21)^{3} (0.79)^{2}

1 point

There are 7 black and 20 blue pens in a box. A pen is chosen at random, and its colour is noted. If the process repeats independently, 13 times with replacement, then calculate the expected number of black pens chosen?

27 91

27 260

20 169

20 91

Number of calls received at an office follows a Poisson distribution with an average of 1 call per minute. Find the probability that no call will be received in two minutes at the office. (Enter the answer correct to 2 decimal accuracy.)

1 point

A quiz team is to be chosen randomly from 6 boys and 4 girls. The team has 3 slots which are to be filled randomly. If

X

denotes the number of boys in the quiz team, then using the given information, answer questions (12) and (13).

Calculate

P (X = 2)

. (Enter the answer correct to 2 decimal places)

1 point

Calculate the value of

E (X)

. (Enter the answer correct to 2 decimal places)

English Week 11 Graded Assignments IIT Madras

Khushi Dii — Tue, 15 Aug 2023 14:37:25 +0000

Maths Week 11 Graded Assignments IIT Madras

Khushi Dii — Tue, 15 Aug 2023 14:31:19 +0000

CT Week 11 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 04:24:56 +0000

Computational Thinking week 11 graded assignment Complete Questions Are Discussed In This Blog. Access From Below Link

1.reverse is a recursive procedure to reverse a list. Select the correct code fragment to complete the pseudocode given below. It is a Multiple Select Question (MSQ).

 
 
 
 
Procedure reverse(L)
    if(length(L) <= 1){
        return(L)
    }
     *********************
      * Fill the code *
     *********************
End reverse
 

return([last(L)] ++ reverse(init(L)))

return([first(L)] ++ reverse(rest(L)))

return([last(L)] ++ reverse(init(rest(L))) ++ [first(L)])

return([first(L)] ++ reverse(init(rest(L))) ++ [last(L)])

return([last(L)] ++ reverse(rest(init(L))) ++ [first(L)])

Question:2-4:

An auto-grading system for an online course is designed in the following way:

∙

A student’s submission is recorded as a dictionary with the following keys

\circ

The “roll” key maps to the student’s roll number.

\circ

The “time” key maps to the time of submission

\circ

The “score” key maps to the student’s score for that submission

∙

Each student can make multiple submissions before the deadline.

∙

Every time a student makes a submission, the dictionary corresponding to it is appended to the end of a list called scores.

An example:

 
scores =   [{“roll”: 12, “time”: 10:20, “score”: 80 },
            {“roll”: 20, “time”: 11:23, “score”: 70 },
            {“roll”: 12, “time”: 20:40, “score”: 90 },
            {“roll”: 12, “time”: 23:50, “score”: 95 },
            {“roll”: 20, “time”: 23:53, “score”: 65 }]

Study the following pseudocode:

 
Procedure isPresent(L, roll)
    foreach D in L{
        if(D[“roll”] == roll){
            return(True)
        }
    }
    return(False)
End isPresent

 
 
 
 
 
Procedure getSubs(L)
    firstSub = {}, restSub = []
    if(length(L) <= 1){
        return(L)
    }
    firstSub = first(L)
    restSub = rest(L)
    if(isPresent(restSub, firstSub[“roll”])){
        return(getSubs(restSub))
    }
    else {
        return([firstSub] ++ getSubs(restSub))
    }
End getSubs
 

Answer questions 2 to 4 after executing the pseudocode given below:

 
submisssions = []
  
scores = [ {“roll”: 12, “time”: 10:20, “score”: 80 },
           {“roll”: 20, “time”: 11:23, “score”: 70 },
           {“roll”: 12, “time”: 20:40, “score”: 90 },
           {“roll”: 12, “time”: 23:50, “score”: 95 },
           {“roll”: 20, “time”: 23:53, “score”: 65 } ]
    
submisssions = getSubs(scores)

4 points

2. What is the value of submissions?

[ {“roll”: 12, “time”: 10:20, “score”: 80 },

{“roll”: 20, “time”: 11:23, “score”: 70 } ]

[ {“roll”: 20, “time”: 11:23, “score”: 70 },

{“roll”: 12, “time”: 10:20, “score”: 80 } ]

[ {“roll”: 12, “time”: 23:50, “score”: 95 },

{“roll”: 20, “time”: 23:53, “score”: 65 } ]

[ {“roll”: 20, “time”: 23:53, “score”: 65 },

{“roll”: 12, “time”: 23:50, “score”: 95 } ]

4 points

3.What does the variable submissions represent?

The list of all the submissions made by the students sorted in the ascending order of time.

The list of all the submissions made by the students sorted in the descending order of time.

The list of the last submissions made by the students sorted in the ascending order of time.

The list of the last submissions made by the students sorted in the descending order of time.

The list of the first submissions made by the students sorted in the ascending order of time.

The list of the first submissions made by the students sorted in the descending order of time.

4 points

4.Assume that reverse is a procedure that reverses a list. Which of the following statements returns the list of the first submissions made by the students sorted in the ascending order of time?

getSubs(scores)

reverse(getSubs(scores))

getSubs(reverse(scores)))

reverse(getSubs(reverse(scores)))

4 points

5.outcomes is a list of strings that contains the information about the outcome of cricket matches played by India in a tournament. Assume that each element in the list is either “win” or “loss”. For example, if five matches have been played, then outcomes could look like this:

[“won”, “lost”, “lost”, “won”, “won”]

We call a list of outcomes a blank slate if the number of wins is equal to the number of losses. blankSlate is a procedure that accepts outcomes as input and returns True if it is a blank slate and False otherwise. Select the correct code fragment to complete the following pseudocode. It is a Multiple Select Question (MSQ).

 
 
 
 
Procedure blankSlate(outcomes)
    if(numeric(outcomes) == 0){
        return(True)
    }
    else{
        return(False)
    }
End blankSlate
  
*********************
* Fill the code *
*********************
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return(0)
    }
    if(last(L) == “won”){
        return(numeric(init(L)) + 1)
    }
    else{
        return(numeric(init(L)) − 1)
    }
End numeric
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return (0)
    }
    if(last(L) == “won”){
        return(numeric(rest(L)) + 1)
    }
    else{
        return(numeric(rest(L)) − 1)
    }
End numeric
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return(0)
    }
    if(first(L) == “won”){
        return(numeric(rest(L)) + 1)
    }
    else{
        return(numeric(rest(L)) − 1)
    }
End numeric
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return(0)
    }
    if(first(L) == “won”){
        return(numeric(init(L)) + 1)
    }
    else{
        return(numeric(init(L)) − 1)
    }
End numeric
 

QUESTION-6-7

2n chess players are participating in a tournament. Each player is given a unique participant ID that is represented as a string. The player IDs are stored in a non-empty list players in the descending order of their rating, i.e., the first element in the list has the ID of the player with the highest rating.

The matches are scheduled as follows: The $i^{t h}$ match is between the $i^{t h}$ player from the top and the $i^{t h}$ player from the bottom of the rating list. We wish to create a list called matches which stores the sequences of matches, starting with the first match and ending with the last match. Each match is represented as a list of two players, the first element of which is the ID of the player with the higher rating, while the second element is the ID of the player with lower rating. Assume that no two players have the same rating.

Answer questions 6 and 7 based on this information.

4 points

matchThem is a recursive procedure that accepts players as argument and returns matches. Select the correct implementation of the procedure. It is a Multiple Select Question (MSQ).

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 2){
        return([players])
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 2){
        return(players)
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 0){
        return([])
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 0){
        return([players])
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

3 points

7.matchThem is a non-recursive procedure that accepts players as argument and returns matches. Select the correct implementation of the procedure.

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) > 0){
        matches = matches ++ [[last(players), first(players)]]
        players = rest(init(players))
    }
    return(matches)
End matchThem

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) > 0){
        matches = matches ++ [[first(players), last(players)]]
        players = rest(init(players))
    }
    return(matches)
End matchThem

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) >= 0){
        matches = matches ++ [[first(players), last(players)]]
        players = rest(init(players))
    }
    return(matches)
End matchThem

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) > 0){
        matches = matches ++ [[first(players), last(players)]]
        players = rest(players)
    }
    return(matches)
End matchThem

Question 8-11

Consider the following graph with six nodes. A is a 6 × 6 matrix corresponding to this graph. Assume that it has already been computed:

In the following pseudocode:

graph is a matrix
parents is a dictionary
sequence is a list

 
 
 
 
 
Procedure DFS(graph, parents, sequence, i)
    sequence = sequence ++ [i]
    foreach j in columns(graph){
        if(graph[i][j] == 1 and not(isKey(parents, j))){
            parents[j] = i
            parents, sequence = DFS(graph, parents, sequence, j)
        }
    }
    return(parents, sequence)
End DFS
 

Answer questions 8 to 11 using the information given above. In all questions, S represents a list, P represents a dictionary, while A and B represent matrices.

4 points

8.What will be the value of S after executing the following pseudocode?

 
P = { }
S = [ ]
P[0] = -1
P, S = DFS(A, P, S, 0)

[0, 1, 2, 5, 3, 4]

[0, 1, 4]

[0, 1, 2, 3, 5, 4]

[0, 3, 1, 4, 5]

3 points

9.What will be the value of nodes after executing the following pseudocode?

 
P = { }
S = [ ], nodes = []
P[5] = -1
P, S = DFS(A, P, S, 5)
nodes = keys(P)

[5, 2, 1, 0, 3, 4]

[5, 2, 1, 4, 0, 3]

[5, 2, 3, 0, 1, 4]

Cannot be determined

3 points

10.Assume that sort is a procedure that accepts a list of integers as input and returns a sorted list in ascending order. If 0 ≤ start ≤ 5, which of the following statements are true at the end of execution of the following pseudocode? It is a Multiple Select Question (MSQ).

 
P = { }
S = [], nodes = []
P[start] = -1
P, S = DFS(A, P, S, start)
nodes = sort(keys(P))

nodes is equal to [0, 1, 2, 3, 4, 5]

S is equal to [0, 1, 2, 3, 4, 5]

The value of nodes is independent of start

The value of S is independent of start

The graph is connected.

The graph is not connected.

4 points

11.Execute the following pseudocode

 
 
 
 
P = { }
S = [ ]
P[3] = -1, parent = 0
P, S = DFS(A, P, S, 3)
B = createMatrix(6, 6)
foreach i in keys(P){
    if(i != 3){
        parent = P[i]
        B[parent][i] = 1
    }
}
 

Correct Answer