IIT Madras Graded Assignments – Students Community

Statistics Week 10 Graded Assignments

Khushi Dii — Sat, 12 Aug 2023 04:22:00 +0000

Statistics Week 10 graded assignment Complete Solutions Key Given In This Page Check Below . We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons If Not Able To Complete Graded Assignments

There are

2^{6}

numbered cards in a deck among which

^{6} �_{�}

cards bear the number

�; � = 0, 1, 2, . . ., 6

. From the deck, 10 cards are drawn with replacement. What is the expectation of the sum of their numbers?(Enter the answer correct to 1 decimal accuracy)

1 point

An unbiased die is thrown 13 times. After each throw a ‘+’ is recorded for 2 or 5 and ‘-‘ is recorded for 1,3,4 or 6, the signs forming an ordered sequence. To each, except the first and last sign, a random variable

�_{�}; � = 1, 2, . . ., 11

is associated which takes the value

1

if both of its neighbouring sign differs from the one between them and

0

otherwise. If the random variable

�

is defined as

� = 3 � + 13

where,

� = \sum_{� = 1}^{11} �_{�}

.
Find the expected value of

�

\frac{183}{9}

\frac{139}{9}

\frac{22}{9}

\frac{66}{9}

1 point

�_{�}; � = 1, 2, . . ., 11

is associated which takes the value

1

if both of its neighbouring sign differs from the one between them and

0

otherwise. If the random variable

�

is defined as

� = 3 � + 13

where,

� = \sum_{� = 1}^{11} �_{�}

.
Which of the following statement(s) is/are true?

� (�) = 3 � (�) + 13

� (�) = 9 � (�)

� (�) = 9 � (�) + 13

� (�) = 9 � (�) + 13

1 point

Amandeep is in the middle of a bridge of infinite length. He takes the unit step to the right with probability 0.66 and to the left with probability 0.34. Assume that the movements are independent of each other.
Hint: Consider the random variable

�_{�}

associated with the

�^{� ℎ}

step defined as:

�_{�}

{\begin{cases} 1 & if the step of Amandeep is towards the right \\ - 1 & if the step of Amandeep is towards the left \end{cases}

What is the expected distance between the starting point and end point of Amandeep after 5 steps?

- 0.32

1.6

- 1.6

0.32

1 point

�_{�}

associated with the

�^{� ℎ}

step defined as:

�_{�}

{\begin{cases} 1 & if the step of Amandeep is towards the right \\ - 1 & if the step of Amandeep is towards the left \end{cases}

What is the variance distance between the starting point and end point of Amandeep after 5 steps?

4.49

0.9

1.56

1

A box contains 10 white and 6 black balls. 2 balls are drawn at random without replacement. Find the expected value of the number of white balls drawn. (Enter the answer correct to 2 decimal places)

1 point

Rohit wants to open his door with

5

keys(out of which

1

will open the door) and tries the keys independently and at random. If unsuccessful keys are eliminated from further selection, then Find the expected number of trials required to open the door.
Hint: Suppose Rohit gets the first success at

�^{� ℎ}

trial, i.e., he is unable to open the door in the first

(� - 1)

trials.
And, P(he gets first success at second trial)=

(1 - \frac{1}{5}) \times \frac{1}{4}

�

and

�

are independent random variables with means 14 and 20, and variances 2 and 6 respectively. Find the variance of

3 � + 6 �

1 point

Table Q10.1.G. represents the probability mass function of a random variable X

Table Q10.1.G: Probability Mass Function
$�$	-1	4	5
$� (� = �)$	$\frac{1}{6}$	$\frac{1}{3}$	$\frac{9}{18}$

Calculate the value of

� (2 � + 1)^{2}

. (Enter the answer correct to 2 decimal places)

1 point

Suppose that

�

is a random variable for which

� (�) = 15

and

� � � (�) = 22

. Find the positive values of

�

and

�

such that

� = � � - �

, has expectation

0

and variance

1

\frac{- 1}{\sqrt{22}}

\frac{- 15}{\sqrt{22}}

1

15

\frac{1}{22}

\frac{15}{\sqrt{22}}

\frac{1}{\sqrt{22}}

\frac{15}{\sqrt{22}}

CT Week 10 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 04:21:00 +0000

Computational Thinking week 10 graded assignment Complete Solutions Are Discussed In This Blog. We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons If Not Able To Complete Graded Assignments

1.The following pseudocode is executing using the “Scores” table. At the end of the execution, matrix represents the adjacency matrix of the graph generated from the “Scores” table.

 
 
 
 
D = {}
while(Table 1 has more rows){
    Read the first row X in Table 1
    D[X.SeqNo] = {"P": X.Physics, "C": X.Chemistry, "M": X.Mathematics}
    Move X to Table 2
}
matrixPh = getAdjMatrix(D, "P")
matrixCh = getAdjMatrix(D, "C")
matrixMa = getAdjMatrix(D, "M")
  
Procedure getAdjMatrix(D, Subject)
    n = length(keys(D))
    matrix = createMatrix(n, n)
    foreach i in rows(matrix){
        foreach j in columns(matrix){
            if(i != j){
                diff = D[i][Subject] - D[j][Subject]
                if(10 <= diff and diff <= 20){
                    matrix[i][j] = 1
                }
            }
        }
    }
    return(matrix)
End getAdjMatrix
 

5 points

If matrixPh[i] [j] = 1, then

i scored at most 10 and at least 20 more marks in Physics than j

i scored at least 10 and at most 20 more marks in Physics than j

j scored at least 10 and at most 20 more marks in Physics than i

j scored at most 10 and at least 20 more marks in Physics than i

5 points

2.Choose the correct statement based on above pseudocode.

For all i, j with i

≠

$\neq =$ j, matrixPh[i][j] + matrixPh[j][i] = 1

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 1 then matrixPh[j][i] = 0

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 0 then matrixPh[j][i] = 1

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 1 then matrixPh[j][i] = 1

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 0 then matrixPh[j][i] = 0

5 points

3.Consider the dictionary D, and the matrices matrixPh, matrixCh and matrixMa computed in the previous question. The following pseudocode generate the adjacency matrix matrixHelp.

 
n = length(keys(D))
matrixHelp = createMatrix(n, n)
    foreach i in rows(matrixHelp){
        foreach j in columns(matrixHelp){
            matrixHelp[i][j] = matrixCh[i][j] + matrixPh[i][j] + matrixMa[i][j]
        }
}

Let i and j be indices of two students. Choose the correct statement(s) from the given options. It is a Multiple Select Question (MSQ)

0 <= matrixHelp[i][j] <= 3

matrixHelp[i][j] + matrixHelp[j][i] <= 3

matrixHelp[i][j]

≠

$\neq =$ matrixHelp[j][i]

if matrixHelp[i][j] = 0, then matrixHelp[j][i] = 3

if matrixHelp[i][j] = 3, then matrixHelp[j][i] = 0

5 points

4.At the end of the following pseudocode, A captures the number of distinct pairs of students who can help each other in at least one subject, and B captures the number of distinct pairs of students where one can help the other in all subjects. Choose the correct code fragment to complete the pseudocode.

 
 
 
 
A = 0, B = 0
foreach i in rows(matrixHelp){
    foreach j in columns(matrixHelp){
        ***********************
         *** Fill the code ***
        ***********************
    }
}
 

 
if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){
    A = A + 1
}
if(matrixHelp[i][j] == 3){
    B = B + 1
}

 
if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){
    A = A + 1
}
if(matrixHelp[i][j] > 2){
    B = B + 1
}

 
if(i < j){
    if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){
       A = A + 1
    }
    if(matrixHelp[i][j] > 2){
       B = B + 1
    }
}

 
if(i < j){
    if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){
       A = A + 1
    }
}
if(matrixHelp[i][j] > 2){
    B = B + 1
}

Question (5-8)
The following table contains information regarding books in a library. Each entry in the table corresponds to a book and is authored by at least two authors. There is a pool of n authors, each author being assigned a unique index between 0 and n − 1. There are M books in total.

The table is represented by a dictionary named books, with the keys as serial numbers and values as the corresponding list of authors. Assume that books has already been computed. For example, we have: books[0] = [0, 2, 3]. Consider the followig question.

5 points

4.The following pseudocode generates a graph G from books. Each node corresponds to an author. There is an edge between two different authors i and j if they have co-authored a book, and the edge is labeled with the number of books they have co-authored. Choose the correct code fragment to complete the following pseudocode.

 
 
 
 
matrix = createMatrix(n, n)
foreach i in keys(books){
    foreach j in books[i]{
        foreach k in books[i]{
           ***********************
            *** Fill the code ***
           ***********************        
        }
    }
}
 

 
matrix[j][k] = matrix[j][k] + 1

 
if(j != k){
    matrix[j][k] = matrix[j][k] + 1
}

 
if(j != k){
    matrix[j][k] = matrix[j][k] + 1
    matrix[k][j] = matrix[k][j] + 1
}

 
matrix[j][k] = matrix[j][k] + 1
matrix[k][j] = matrix[k][j] + 1

5 points

5.The following pseudocode creates adjacency matrix matrix2 of another graph H from books. For two different authors i and j, what does the value matrix2[i][j] represent at the end of the execution?

 
 
 
 
matrix2 = createMatrix(n, n)
foreach j in rows(matrix2){
    foreach k in columns(matrix2){
        matrix2[j][k] = []
    }
}
foreach i in keys(books){
    foreach j in book[i]{
        foreach k in books[i]{
            foreach h in books[i]{
                if(j != k and j != h and k != h and not member(matrix2[j][k], h)){
                    matrix2[j][k] = matrix2[j][k] ++ [h]
                    matrix2[k][j] = matrix2[k][j] ++ [h]
                }
            }
        }
    }
}
 

List of authors who have co-authored a book with both i and j

List of authors who have co-authored a book with either i or j

List of authors who have co-authored at least two book with both i and j

List of authors who have co-authored at least two book with either i or j

5 points

6.Which of the following combinations of entries in matrix and matrix2 is possible for two different authors i and j? It is Multiple Select Question (MSQ).

matrix[i] [j] = 0 and matrix2[i] [j] = [ ]

matrix[i][j] = 0 and matrix2[i][j]

≠

$\neq =$ [ ]

matrix[i][j] > 0 and matrix2[i][j] = [ ]

matrix[i][j] > 0 and matrix2[i][j]

≠

$\neq =$ [ ]

5 points

Consider the matrices matrix and matrix2 constructed in the previous questions.

findAuthor(matrix) finds an author who has the maximum number of co-authors. Choose the correct implementation of the procedure findAuthor. It is a Multiple Select Question.

 
 
 
 
 
Procedure findAuthor(M)
    Max = 0
    A = 0
    foreach i in rows(M){
        Sum = 0
        foreach j in columns(M){
            if(M[i][j] > 0){
                Sum = Sum + 1
            }
        }
        if(Sum > Max){
            Max = Sum
            A = i
        }
    }
    return(A)
End findAuthor
 

 
 
 
 
 
Procedure findAuthor(M)
    Max = 0
    A = 0
    foreach i in rows(M){
        Sum = 0
        foreach j in columns(M){
            if(M[i][j] > 0){
                Sum = Sum + M[i][j]
            }
        }
        if(Sum > Max){
            Max = Sum
            A = i
        }
    }
    return(A)
End findAuthor
 

 
 
 
 
 
Procedure findAuthor(M)
    Max = 0
    A = 0
    foreach i in columns(M){
        Sum = 0
        foreach j in rows(M){
            if(M[j][i] > 0){
                Sum = Sum + 1
            }
        }
        if(Sum > Max){
            Max = Sum
            A = i
        }
    }
    return(A)
End findAuthor
 

 
 
 
 
 
Procedure findAuthor(M)
    Max = 0
    A = 0
    foreach i in columns(M){
        Sum = 0
        foreach j in rows(M){
            if(M[j][i] > 0){
                Sum = Sum + M[j][i]
            }
        }
        if(Sum > Max){
            Max = Sum
            A = i
        }
    }
    return(A)
End findAuthor
 

Question (9-10)

The following pseudocode is executing using the “Shopping bills” dataset. Each customer is being assigned a unique index between 0 and n − 1. Dictionary D has already been computed with keys as index and values as list of distinct shops visited by the corresponding customer. Assume that there exists a procedure intersection which takes two lists as input and outputs another list which contains the common elements in the input lists.

 
 
 
 
n = length(keys(D))
matrix = createMatrix(n, n)
foreach i in rows(matrix){
    foreach j in columns(matrix){
        if(i != j){
            matrix[i][j] = intersection(D[i], D[j])
        }
        else{
            matrix[i][j] = []
        }
    }
}
 

5 points

Consider the adjacency matrix matrix constructed above. Assume that there exists a procedure removeDuplicate which receives a list as input and removes all duplicate elements in the list. When will findGoodSet(matrix) return True?

 
 
 
 
Procedure findGoodSet(M)
    foreach i in rows(M){
        foreach j in columns(M){
            foreach h in rows(M){
                list1 = []
                if(length(M[i][j]) == 1 and member(D[h], first(M[i][j]))){
                    list1 = list1 ++ M[i][j]
                }
                if(length(M[i][h]) == 1 and member(D[j], first(M[i][h]))){
                    list1 = list1 ++ M[i][h]
                }
                if(length(M[j][h]) == 1 and member(D[i], first(M[j][h]))){
                    list1 = list1 ++ M[j][h]
                }
                list1 = removeDuplicate(list1)
                if(length(list1) == 1){
                    return(True)
                }
            }
        }
    }
    return(False)
End findGoodSet
 

If there exists three customers who have visited all three shops.

If there exist three customers such that every pair of customers among them have visited only one and the same shop in common.

If there exists three customers who have visited exactly one shop.

If there exists three customers where each pair among them have visited exactly one shop in common.

5 points

10.For a pair of customers i and j, j is said to be shopping partner of i if i and j have visited at least two shops in common. findTopCustomer(matrix) finds a customer who has the maximum shopping partners. Choose the correct implementation of findTopCustomer.

 
 
 
 
 
Procedure findTopCustomer(M)
    Max = 0, A = 0
    foreach i in rows(M){
        C = 0
        foreach j in columns(M) {
            if(length(M[i][j]) == 2){
               C = C + 1
            }
        }
        if(C > Max){
           Max = C
           A = i
        }
    }
    return(A)
End findTopCustomer
 

 
 
 
 
 
Procedure findTopCustomer(M)
    Max = 0, A = 0
    foreach i in rows(M){
        C = 0
        foreach j in columns(M){
            if(length(M[i][j]) > 1){
               C = C + 1
            }
        }
        if(C > Max){
           Max = C
           A = i
        }
    }
    return(A)
End findTopCustomer
 

 
 
 
 
 
Procedure findTopCustomer(M)
    Max = 0, A = 0
    foreach i in rows(M){
        C = 0
        foreach j in columns(M) {
            if(length(M[i][j]) == 2){
               C = C + 1
            }
        }
        if(C > Max){
           Max = C
           A = i
        }
    }
    return(Max)
End findTopCustomer
 

 
 
 
 
 
Procedure findTopCustomer(M)
    Max = 0, A = 0
    foreach i in rows(M){
        C = 0
        foreach j in columns(M){
            if(length(M[i][j]) > 1){
               C = C + 1
            }
        }
        if(C > Max){
           Max = C
           A = i
        }
    }
    return(Max)
End findTopCustomer

English Week 10 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 04:20:00 +0000

Maths Week 10 Graded Assignments IIT Madras

KHUSHI — Sat, 12 Aug 2023 04:16:00 +0000

English Week 9 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 04:00:00 +0000

Statistics Week 9 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 03:52:00 +0000

CT Week 9 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 03:42:00 +0000

Computational Thinking week 9 graded assignment Complete Questions Are Discussed In This Blog. Access From Below Link

Consider a graph generated from the “Scores” table that is represented by a matrix B. Each node in the graph corresponds to a student from the table. SeqNo is used to label the nodes in the graph. Study the given pseudocode and answer the following questions.

 
 
 
 
A = {}
while(Table 1 has more rows){
    Read the first row X in Table 1
    A[X.SeqNo] = [X.CityTown, X.Gender]
    Move X to Table 2
}
n = length(keys(A))
B = createMatrix(n, n)
foreach i in keys(A){
    foreach j in keys(A){
        if(i != j and isRelated(A[i], A[j])){
            B[i][j] = 1
        }
    }
}
 Procedure isRelated(x, y)
    if(first(x) == first(y) and last(x) == last(y)){
        return(True)
    }
    else{
        return(False)
    }
End isRelated
 

1.There is an edge between students i and j, with i $\neq =$ j, if and only if:

they are from the same city/town

they have the same gender

they are from the same city/town and have the same gender

they are from the same city/town or have the same gender

2. Which of the following statements are true about this graph? It is a Multiple Select Question (MSQ).

There are two cliques in this graph, one for each gender

In every clique, there is at least a pair of students having different genders

All students in a given clique have the same gender

All students in a given clique are from the same city/town

There are no cliques in this graph

3. The following table contains information regarding books in a library. Each row in the table corresponds to a book and is authored by exactly two authors, with equal contributions from both. There is a pool of n authors, each author being assigned a unique index between 0 and $n - 1$ . There are M books in total.

books[0] = [4, 0]

A graph G is generated from this table. Each node corresponds to an author. There is an edge between authors i and j if and only if they have collaborated on a book. Given a pair of authors (i, j), with i $\neq =$ j, what does the value colab[i] [j] represent at the end of the execution of the following pseudocode? Assume that the number of authors, n, is given to you.

 
 
 
 
colab = createMatrix(n, n)
auth1 = 0, auth2 = 0
foreach i in keys(books){
    auth1 = first(books[i])
    auth2 = last(books[i])
    colab[auth1][auth2] = colab[auth1][auth2] + 1
    colab[auth2][auth1] = colab[auth2][auth1] + 1
}
 

It represents the number of books published by authors i or j

It represents the number of books in which authors i and j have collaborated

It represents the number of books published by author i + number of books published by author j

It represents the number of books published by author i in which he has not collaborated with author j

Question-(4 to 11)
Using the matrix colab computed from the previous problem, answer the following questions. For each question, what do the variables aVar and bVar represent at the end of execution of the pseudocode? Pick the correct option from the table given below.

 
 
 
 
 
aVar = 0
bVar = []
foreach r in rows(colab){
    foreach c in columns(colab){
        if (colab[r][c] > aVar){
            aVar = colab[r][c]
            bVar = [r, c]
        }
    }
}
 

4. What is the correct option for variable aVar?

5.What is the correct option for variable bVar?

 
 
 
 
 
aVar = 0
bVar = 0
foreach r in rows(colab){
    count = 0
    foreach c in columns(colab){
        if (colab[r][c] > 0){
            count = count + 1
        }
    }
    if(count > aVar){
        aVar = count
        bVar = r
    }
}
 

6.What is the correct option for variable aVar?

7.What is the correct option for variable bVar?

 
 
 
 
 
aVar = 0
bVar = 0
foreach r in rows(colab){
    count = 0
    foreach c in columns(colab){
        count = count + colab[r][c]
    }
    if(count > aVar){
        aVar = count
        bVar = r
    }
}
 

8.What is the correct option for variable aVar?

9. What is the correct option for variable bVar?

 
 
 
 
aVar = 0
bVar = []
foreach r in rows(colab){
    count = 0
    foreach c in columns(colab){
        if (colab[r][c] > 0){
            count = count + 1
        }
    }
    if(count == 1){
        aVar = aVar + 1
        bVar = bVar ++ [r]
    }
}
 

10.What is the correct option for variable aVar?

100 point

11.What is the correct option for variable bVar?

Continuing with the previous question, authors is a list of authors. isClique is a procedure that determines if every pair of authors in this list have collaborated at least once. It returns False if at least one pair of authors haven’t collaborated, and True if every pair of authors have collaborated at least once. Select the correct code fragment to complete the pseudocode. It is a Multiple Select Question (MSQ).

 
 
 
 
Procedure isClique(authors, colab)
    foreach i in authors{
        foreach j in authors{
            *********************
            *   Fill the code   *
            *********************
        }
    }
    return(True)
End isClique
 

 
if(i != j and colab[i][j] > 0){
    return(False)
}

 
if (i != j and colab[i][j] == 0){
    return(False)
}

 
if(i != j){
    if(colab[i][j] == 1){
        return (False)
    }
}

 
if(i != j){
    if(colab[i][j] == 0){
        return(False)
    }
}

 
if(i != j){
    if(colab[i][j] == 0){
        return(True)
    }
}

A computer scientist is planning to conduct an event in the city. She has come up with a novel scheme to invite people:

The host (computer scientist) can send out any number of invitations and does not accept any invitation.

Each invitation is represented by a unique text message.
Each invitee can choose to either accept or reject the invitation.
If an invitee accepts the invitation, then he can invite exactly one other person by forwarding the invitation that he received to this person, i.e., the invitee can forward the message he received only once.
If an invitee doesn’t accept the invitation, he cannot invite anyone.
If a person receives multiple invitations, he can accept at most one of them. All other invitations must be rejected.

This situation is modeled as a graph. There is a node corresponding to every person who attends the event. n people attend the event and the attendees are indexed from 0 to $n - 1$ . Given a pair of attendees (i, j), there is an edge from i to j if and only if the following conditions are satisfied:

j was invited by i
j accepted i‘s invitation

The graph is represented by a matrix A, such that A[i] [j] = 1 if and only if there is an edge from i to j.

For the case of n = 5, which of the following is a possible representation of the graph?

correct answer

4 points

Continuing with the previous question, for a pair of attendees (i, j) other than the host, we say that i is the ancestor of j, if their messages are identical and i has accepted the invitation before j. Note that each invitation sent out by the host is a unique text message. Assume that the matrix A that represents the graph has already been computed.

isAncestor is a procedure that accepts the matrix A and two attendees i and j other than the host as input, with i $\neq =$ j, and returns True if i is the ancestor of j, and False otherwise. Select the correct code fragment to complete the pseudocode.

 
 
 
 
Procedure isAncestor(A, i, j)
      k = i
      flag = True
      while(flag){
           flag = False
           foreach c in columns(A){
               *********************
                  * Fill the code *
               *********************
           }
       }
       return(False)
 End isAncestor
 

 
if(A[k][c] == 1){
    if(c == j){
        return(True)
    }
    k = c
    exitloop
}

 
if(A[k][c] == 1){
    if(c == j){
        return (True)
    }
    flag = True
    exitloop
}

 
if(A[k][c] == 1){
    if(c == j){
        flag = True
        return(True)
    }
    k = c
    exitloop
}

 
 
 
 
 
if(A[k][c] == 1){
    if(c == j){
        return(True)
    }
    k = c
    flag = True
    exitloop
}

Maths Week 9 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 03:39:00 +0000

Maths Week 9 Graded Assignments Questions Are Different So Do From Master Key Access Below Any Doubt Feel Free To Comment And Ask Some Questions Are Same

IIT Madras Graded Assignments – Students Community

Statistics Week 10 Graded Assignments

CT Week 10 Graded Assignments IIT Madras

English Week 10 Graded Assignments IIT Madras

Maths Week 10 Graded Assignments IIT Madras

Maths week 10 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

English Week 9 Graded Assignments IIT Madras

Statistics Week 9 Graded Assignments IIT Madras

Week 9 Graded Assignments IIT Madras

CT Week 9 Graded Assignments IIT Madras

Maths Week 9 Graded Assignments IIT Madras