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May 2026 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II Quiz 2: 16 August 2026 (May 2026 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 2 paper sat on 16 Aug 2026, in the May 2026 term: 26 questions for 47 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
26
Marks
47
Duration
120 min
MCQ
4
MSQ
2
Written
20
Take as mock testPractise with answers

Updated

Official paper: Statistics2 14 Aug 26 · No negative marking.

Question 1

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

Show answer

Correct answer

  • A

    Useful Data has been mentioned above.

Question 1 on its own page

Question 2

+3 marksOne or more correct options

Let are three independent and identically distributed random variables with mean and variance . Given below are 3 different formulations. Which of the following option(s) is/are correct?

Select all that apply.

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answers

  • A

    —

  • B

    —

  • D

    —

Question 2 on its own page

Question 3

+3 marksOne correct option

Let . Define a random variable as

Find the CDF of .

Let . Define a random variable as
  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 3 on its own page

Question 4

+3 marksWritten answer

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

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A written answer, not marked automatically.

Question 4 on its own page

Question 5

+3 marksWritten answer

Let and be discrete random variables with the joint probability mass function,

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

Let and be discrete random variables with the joint probability mass function,
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A written answer, not marked automatically.

Question 5 on its own page

Question 6

+0.5 marksWritten answer

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of 180 hours. By using Central limit theorem, a quality engineer computes the probability that the average lifetime of a random sample of bulbs is greater than 1230 hours to be approximately 0.07. What is the minimum sample size taken by the engineer ? Solution: Let represents lifetime of an individual bulb with mean =1200 and standard deviation =180. Let be the average lifetime of samples. Therefore, and are and respectively. We are given that, By using CLT, On comparing with Z-values, Consider the following options for the blanks.

Answer the given sub-questions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of

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 factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of 180 hours. By using Central limit theorem, a quality engineer computes the probability that the average lifetime of a random sample of bulbs is greater than 1230 hours to be approximately 0.07. What is the minimum sample size taken by the engineer ? Solution: Let represents lifetime of an individual bulb with mean =1200 and standard deviation =180. Let be the average lifetime of samples. Therefore, and are and respectively. We are given that, By using CLT, On comparing with Z-values, Consider the following options for the blanks.

Answer the given sub-questions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of

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 factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of 180 hours. By using Central limit theorem, a quality engineer computes the probability that the average lifetime of a random sample of bulbs is greater than 1230 hours to be approximately 0.07. What is the minimum sample size taken by the engineer ? Solution: Let represents lifetime of an individual bulb with mean =1200 and standard deviation =180. Let be the average lifetime of samples. Therefore, and are and respectively. We are given that, By using CLT, On comparing with Z-values, Consider the following options for the blanks.

Answer the given sub-questions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of

Enter the correct option number for .

Show answer

A written answer, not marked automatically.

Question 8 on its own page

Question 9

+0.5 marksWritten answer

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of 180 hours. By using Central limit theorem, a quality engineer computes the probability that the average lifetime of a random sample of bulbs is greater than 1230 hours to be approximately 0.07. What is the minimum sample size taken by the engineer ? Solution: Let represents lifetime of an individual bulb with mean =1200 and standard deviation =180. Let be the average lifetime of samples. Therefore, and are and respectively. We are given that, By using CLT, On comparing with Z-values, Consider the following options for the blanks.

Answer the given sub-questions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of

Enter the correct option number for .

Show answer

A written answer, not marked automatically.

Question 9 on its own page

Question 10

+1 markWritten answer

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of 180 hours. By using Central limit theorem, a quality engineer computes the probability that the average lifetime of a random sample of bulbs is greater than 1230 hours to be approximately 0.07. What is the minimum sample size taken by the engineer ? Solution: Let represents lifetime of an individual bulb with mean =1200 and standard deviation =180. Let be the average lifetime of samples. Therefore, and are and respectively. We are given that, By using CLT, On comparing with Z-values, Consider the following options for the blanks.

Answer the given sub-questions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of

Calculate the value for .

Show answer

A written answer, not marked automatically.

Question 10 on its own page

Question 11

+3 marksOne or more correct options

Let , where . Based on the above data, answer the given subquestions.

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

Select all that apply.

  1. A

    Uniform[1,4]

  2. B

    Uniform[4,7]

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

Correct answers

  • A

    Uniform[1,4]

  • C
    Figure from the original question paper
  • D
    Figure from the original question paper
Question 11 on its own page

Question 12

+2 marksWritten answer

Let , where . Based on the above data, answer the given subquestions.

What is the value of ? Enter the answer correct to one decimal place.

Show answer

A written answer, not marked automatically.

Question 12 on its own page

Question 13

+2 marksOne correct option

Let . Suppose that and Based on the above data, answer the given subquestions.

What is the marginal density of ?

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • A

    —

Question 13 on its own page

Question 14

+3 marksWritten answer

Let . Suppose that and Based on the above data, answer the given subquestions.

Find Enter the answer correct to two decimal places.

Show answer

A written answer, not marked automatically.

Question 14 on its own page

Question 15

+3 marksOne correct option

Let

. Define a centralised random variable where . Based on the above data, answer the given subquestions.

Let

Find the moment generating function (MGF) of , where

.

Find the moment generating function (MGF) of , where
  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
Question 15 on its own page

Question 16

+2 marksWritten answer

Let

. Define a centralised random variable where . Based on the above data, answer the given subquestions.

Let

Inscript Find the value of , where

. Enter the answer correct to two decimal places.

Inscript Find the value of , where
Show answer

A written answer, not marked automatically.

Question 16 on its own page

Question 17

+3 marksWritten answer

Let be i.i.d random variables with mean 10 and variance 25. Based on the above data, answer the given subquestions.

Find the value of

.

Find the value of
Show answer

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Question 17 on its own page

Question 18

+2 marksWritten answer

Let be i.i.d random variables with mean 10 and variance 25. Based on the above data, answer the given subquestions.

Find the value of Var , where

. Enter the answer correct to three decimal places.

Find the value of Var , where
Show answer

A written answer, not marked automatically.

Question 18 on its own page

Question 19

+2 marksWritten answer

Let represent the amount of rainfall (in cm) received on a particular day in a city. The PDF of is

Based on the above data, answer the given subquestions.

Let represent the amount of rainfall (in cm) received on a particular day in a city. The PDF of is

What is the probability that the rainfall on a day is between 2 cm and 4 cm? Enter the answer correct to two decimal places.

Show answer

A written answer, not marked automatically.

Question 19 on its own page

Question 20

+3 marksWritten answer

Let represent the amount of rainfall (in cm) received on a particular day in a city. The PDF of is

Based on the above data, answer the given subquestions.

Let represent the amount of rainfall (in cm) received on a particular day in a city. The PDF of is

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

Show answer

A written answer, not marked automatically.

Question 20 on its own page

Question 21

+1 markWritten answer

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of 180 hours. By using Central limit theorem, a quality engineer computes the probability that the average lifetime of a random sample of bulbs is greater than 1230 hours to be approximately 0.07. What is the minimum sample size taken by the engineer ? Solution: Let represents lifetime of an individual bulb with mean =1200 and standard deviation =180. Let be the average lifetime of samples. Therefore, and are and respectively. We are given that, By using CLT, On comparing with Z-values, Consider the following options for the blanks.

Answer the given sub-questions. Note: Enter only the correct option number (e.g. 8) without any brackets or punctuation.

A factory produces light bulbs. The lifetime of an individual bulb has a mean of 1200 hours and a standard deviation of
Show answer

A written answer, not marked automatically.

Question 21 on its own page

Question 22

+1 markWritten answer

Let , where . 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

Let . Suppose that and 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

Let

. Define a centralised random variable where . Based on the above data, answer the given subquestions.

Let
Show answer

A written answer, not marked automatically.

Question 24 on its own page

Question 25

+1 markWritten answer

Let be i.i.d random variables with mean 10 and variance 25. 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

Let represent the amount of rainfall (in cm) received on a particular day in a city. The PDF of is

Based on the above data, answer the given subquestions.

Let represent the amount of rainfall (in cm) received on a particular day in a city. The PDF of is
Show answer

A written answer, not marked automatically.

Question 26 on its own page