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May 2026 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II Quiz 1: 19 July 2026 (May 2026 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 1 paper sat on 19 Jul 2026, in the May 2026 term: 24 questions for 46 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
24
Marks
46
Duration
120 min
MCQ
5
Written
19
Take as mock testPractise with answers

Updated

Official paper: Statistics2 16 Jul 26 · No negative marking.

Question 1

+1 markOne correct option
Figure from the original question paper
Figure from the original question paper
  1. A

    Useful Data has been mentioned above.

  2. B

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

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Correct answer

  • A

    Useful Data has been mentioned above.

Question 1 on its own page

Question 2

+3 marksWritten answer

Let X be a continuous random variable with PDF as follows:

Find the value of a.

Let X be a continuous random variable with PDF as follows:
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Question 3

+3 marksWritten answer

Let and be two independent random variables such that Let another random variable be defined as Find the value of Enter the answer correct to two decimal places.

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Question 4

+3 marksWritten answer

A number from 00 to 99 is selected uniformly at random.The numbers 0 to 9 are treated as two digit numbers and denoted as 00 to 09. Let, • be the digit in the units place, • be the remainder when the number is divided by 4. Find the value of . Enter the answer correct to two decimal places.

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Question 5

+3 marksWritten answer

A random variable has mean 10 and variance 9. Using Chebyshev's inequality, find a lower bound on . Enter the answer correct to two decimal places.

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Question 6

+3 marksWritten answer

A shopping mall issues 400 lucky draw coupons. Among them, one coupon is worth a gift voucher of Rs 2000, one coupon is worth a gift voucher of Rs 1000, and all other coupons are worth Rs 0. If a customer receives 2 coupons drawn at random from the 400, what is the expected value (in Rs) of the prizes won by the customer?

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Question 7

+3 marksOne correct option

Let be a discrete random variable with PMF

Based on the above data, answer the given subquestions.

Let be a discrete random variable with PMF

Find the value of

  1. A
    Figure from the original question paper
  2. B

    —

  3. C
    Figure from the original question paper
  4. D

    —

Show answer

Correct answer

  • C
    Figure from the original question paper
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Question 8

+2 marksWritten answer

Let be a discrete random variable with PMF

Based on the above data, answer the given subquestions.

Let be a discrete random variable with PMF

Using Markov's inequality, obtain an upper bound for Enter the answer correct to two decimal places.

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Question 9

+2 marksOne correct option

Let the random variables i.i.d Uniform{1, 2, 3, 4}. Based on the above data, answer the given subquestions.

What is the value of ?

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • A
    Figure from the original question paper
Question 9 on its own page

Question 10

+3 marksWritten answer

Let the random variables i.i.d Uniform{1, 2, 3, 4}. Based on the above data, answer the given subquestions.

Let find the value of Enter the answer correct to three decimal places.

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Question 11

+3 marksOne correct option

Let be i.i.d random variables with the following probability mass function

Based on the above data, answer the given subquestions.

Let be i.i.d random variables with the following probability mass function

Find the value of .

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • B
    Figure from the original question paper
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Question 12

+2 marksOne correct option

Let be i.i.d random variables with the following probability mass function

Based on the above data, answer the given subquestions.

Let be i.i.d random variables with the following probability mass function

Find the value of .

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answer

  • D
    Figure from the original question paper
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Question 13

+3 marksWritten answer

Let be i.i.d samples of a discrete random variable whose PMF is as follows:

Based on the above data, answer the given subquestions.

Let be i.i.d samples of a discrete random variable whose PMF is as follows:

What is the probability that 1 appears exactly once in the samples? Enter the answer correct to two decimal places.

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Question 14

+2 marksWritten answer

Let be i.i.d samples of a discrete random variable whose PMF is as follows:

Based on the above data, answer the given subquestions.

Let be i.i.d samples of a discrete random variable whose PMF is as follows:

What is the probability that none of the four samples is equal to 0? Enter the answer correct to two decimal places.

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Question 15

+1 markWritten answer

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability density function

Let be the event that a person has to wait for more than 2 minutes and be the event that he has to wait for more than 1 minute. Find the value of .

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den
Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den

Enter the correct option number for .

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Question 16

+1 markWritten answer

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability density function

Let be the event that a person has to wait for more than 2 minutes and be the event that he has to wait for more than 1 minute. Find the value of .

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den
Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den

Enter the correct option number for .

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A written answer, not marked automatically.

Question 16 on its own page

Question 17

+1 markWritten answer

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability density function

Let be the event that a person has to wait for more than 2 minutes and be the event that he has to wait for more than 1 minute. Find the value of .

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den
Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den

Enter the correct option number for .

Show answer

A written answer, not marked automatically.

Question 17 on its own page

Question 18

+1 markWritten answer

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability density function

Let be the event that a person has to wait for more than 2 minutes and be the event that he has to wait for more than 1 minute. Find the value of .

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den
Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den

Enter the correct option number for .

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A written answer, not marked automatically.

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Question 19

+1 markWritten answer

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability density function

Let be the event that a person has to wait for more than 2 minutes and be the event that he has to wait for more than 1 minute. Find the value of .

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den
Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den

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

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Question 20

+1 markWritten answer

Let be a discrete random variable with PMF

Based on the above data, answer the given subquestions.

Let be a discrete random variable with PMF
Show answer

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Question 21

+1 markWritten answer

Let the random variables i.i.d Uniform{1, 2, 3, 4}. Based on the above data, answer the given subquestions.

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Question 21 on its own page

Question 22

+1 markWritten answer

Let be i.i.d random variables with the following probability mass function

Based on the above data, answer the given subquestions.

Let be i.i.d random variables with the following probability mass function
Show answer

A written answer, not marked automatically.

Question 22 on its own page

Question 23

+1 markWritten answer

Let be i.i.d samples of a discrete random variable whose PMF is as follows:

Based on the above data, answer the given subquestions.

Let be i.i.d samples of a discrete random variable whose PMF is as follows:
Show answer

A written answer, not marked automatically.

Question 23 on its own page

Question 24

+1 markWritten answer

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability density function

Let be the event that a person has to wait for more than 2 minutes and be the event that he has to wait for more than 1 minute. Find the value of .

Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den
Suppose that the time (in minutes) that a customer waits at a service counter is a random variable with probability den
Show answer

A written answer, not marked automatically.

Question 24 on its own page