Figure from the original question paper Figure from the original question paper

(A) Useful Data has been mentioned above.

(B) This data attachment is just for a reference & not for an evaluation.

The joint PMF of two discrete random variables and is given as: Based on the above data, answer the given subquestions. The joint PMF of two discrete random variables and is given as: Find the value of .

(D) Figure from the original question paper

(A) Figure from the original question paper

(B) Figure from the original question paper

(C) Figure from the original question paper

The amount of rainfall (in cm) on a randomly chosen rainy day in a city is a continuous random variable with cumulative distribution function Based on the above data, answer the given subquestions. The amount of rainfall (in cm) on a randomly chosen rainy day in a city is a continuous random variable with cumulative Which of the following options correctly represents the probability density function of ?

(D) Figure from the original question paper

(A) Figure from the original question paper

(B) Figure from the original question paper

(C) Figure from the original question paper

Stats 2 Quiz 1 PYQ Jan 2026: 15 Mar 2026 · IITM BS

Question 1

+1 markOne correct option

A
Useful Data has been mentioned above.
B
This data attachment is just for a reference & not for an evaluation.

Show answer

Correct answer

A
Useful Data has been mentioned above.

Question 1 on its own page

Question 2

+3 marksWritten answer

The number of people who make a reservation in a restaurant on a particular day is a random variable with mean equal to 10 and variance equal to 5. Find a lower bound on the probability that on a particular day, number of reservations made will lie in between 5 and 15 using Chebyshev's inequality. Enter the answer correct to two decimal places.

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Question 2 on its own page

Question 3

+3 marksWritten answer

Let and be three random variables with Cov , Cov , Cov , Var Define the new random variables and . Find the value of Cov .

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Question 3 on its own page

Question 4

+3 marksWritten answer

At a bank, the time (in minutes) that a customer waits to be served is a continuous random variable with probability density function

Find the value of .

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Question 4 on its own page

Question 5

+0.5 marksWritten answer

A delivery company operates two independent service counters A and B. Let and denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of and is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for .

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Question 5 on its own page

Question 6

+0.5 marksWritten answer

A delivery company operates two independent service counters A and B. Let and denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of and is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for .

Show answer

A written answer, not marked automatically.

Question 6 on its own page

Question 7

+0.5 marksWritten answer

A delivery company operates two independent service counters A and B. Let and denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of and is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for .

Show answer

A written answer, not marked automatically.

Question 7 on its own page

Question 8

+0.5 marksWritten answer

A delivery company operates two independent service counters A and B. Let and denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of and is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for .

Show answer

A written answer, not marked automatically.

Question 8 on its own page

Question 9

+1 markWritten answer

A delivery company operates two independent service counters A and B. Let and denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of and is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Calculate the value for . Enter the answer correct to one decimal place.

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Question 9 on its own page

Question 10

+3 marksOne or more correct options

A box contains one red ball and one blue ball. Two balls are drawn one after another with replacement and the colour of each ball drawn is recorded. Let • A be the number of times a red ball is drawn in the two draws. • B be the number of times a blue ball is drawn in the two draws. Choose the correct statement(s) from the following.

Select all that apply.

A
The possible values of are {0, 1, 2}
B
The possible values of are {1, 2}
C
D

Show answer

Correct answers

A
The possible values of are {0, 1, 2}
C

Question 10 on its own page

Question 11

+2 marksOne or more correct options

The number of vehicles ( ) passing a signal in a day follows a Poisson distribution with parameter . Each vehicle independently violates traffic rules with probability 0.1. Let denote the number of vehicles violating traffic rules in a day. Based on the above data, answer the given subquestions.

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

Select all that apply.

A
Binomial(15, 0.1)
B
Binomial(30, 0.1)
C
Poisson(0.1)
D
—

Show answer

Correct answers

A
Binomial(15, 0.1)
D
—

Question 11 on its own page

Question 12

+3 marksWritten answer

The number of vehicles ( ) passing a signal in a day follows a Poisson distribution with parameter . Each vehicle independently violates traffic rules with probability 0.1. Let denote the number of vehicles violating traffic rules in a day. Based on the above data, answer the given subquestions.

Find the value of Var(2X)−3Var(Y ) + 4.

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Question 13

+2 marksWritten answer

A small bookstore tracks the number of books sold in an hour. Let a discrete random variable denote the number of books sold in an hour. The probability mass function of is given by:

The store defines a discount indicator as:

Based on the above data, answer the given subquestions.

A small bookstore tracks the number of books sold in an hour. Let a discrete random variable denote the number of books

Find the value of . Enter the answer correct to two decimal places.

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Question 13 on its own page

Question 14

+3 marksWritten answer

A small bookstore tracks the number of books sold in an hour. Let a discrete random variable denote the number of books sold in an hour. The probability mass function of is given by:

The store defines a discount indicator as:

Based on the above data, answer the given subquestions.

Find the value of . Enter the answer correct to two decimal places.

Show answer

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Question 14 on its own page

Question 15

+3 marksOne correct option

A fair coin is tossed three times. Let denote the number of heads in the first toss and be the total number of heads obtained across all three tosses. Based on this, answer the given sub questions:

Find the value of .

A
B
C
D

Show answer

Correct answer

B

Question 15 on its own page

Question 16

+2 marksWritten answer

A fair coin is tossed three times. Let denote the number of heads in the first toss and be the total number of heads obtained across all three tosses. Based on this, answer the given sub questions:

Find the value of . Enter the answer correct to three decimal places.

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Question 17

+3 marksWritten answer

The joint PMF of two discrete random variables and is given as:

Based on the above data, answer the given subquestions.

Find the value of .

Show answer

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Question 17 on its own page

Question 18

+2 marksOne correct option

The joint PMF of two discrete random variables and is given as:

Based on the above data, answer the given subquestions.

Find the value of .

A
B
C
D

Show answer

Correct answer

D

Question 18 on its own page

Question 19

+2 marksOne correct option

The amount of rainfall (in cm) on a randomly chosen rainy day in a city is a continuous random variable with cumulative distribution function

Based on the above data, answer the given subquestions.

Which of the following options correctly represents the probability density function of ?

A
B
C
D

Show answer

Correct answer

D

Question 19 on its own page

Question 20

+3 marksOne correct option

The amount of rainfall (in cm) on a randomly chosen rainy day in a city is a continuous random variable with cumulative distribution function

Based on the above data, answer the given subquestions.

Find the value of .

A
B
C
D

Show answer

Correct answer

A

Question 20 on its own page

Question 21

+1 markWritten answer

A delivery company operates two independent service counters A and B. Let and denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of and is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Show answer

A written answer, not marked automatically.

Question 21 on its own page

Question 22

+1 markWritten answer

The number of vehicles ( ) passing a signal in a day follows a Poisson distribution with parameter . Each vehicle independently violates traffic rules with probability 0.1. Let denote the number of vehicles violating traffic rules in a day. Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 22 on its own page

Question 23

+1 markWritten answer

A small bookstore tracks the number of books sold in an hour. Let a discrete random variable denote the number of books sold in an hour. The probability mass function of is given by:

The store defines a discount indicator as:

Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 23 on its own page

Question 24

+1 markWritten answer

A fair coin is tossed three times. Let denote the number of heads in the first toss and be the total number of heads obtained across all three tosses. Based on this, answer the given sub questions:

Show answer

A written answer, not marked automatically.

Question 24 on its own page

Question 25

+1 markWritten answer

The joint PMF of two discrete random variables and is given as:

Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 25 on its own page

Question 26

+1 markWritten answer

The amount of rainfall (in cm) on a randomly chosen rainy day in a city is a continuous random variable with cumulative distribution function

Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 26 on its own page