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January 2026 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II Quiz 2: 12 April 2026 (January 2026 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 2 paper sat on 12 Apr 2026, in the January 2026 term: 25 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
25
Marks
46
Duration
120 min
MCQ
6
Written
18
MSQ
1
Take as mock testPractise with answers

Updated

Official paper: Statistics2 06 Apr 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
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 correct option

The joint pdf of two continuous random variables and is given by

Are and independent?

The joint pdf of two continuous random variables and is given by
  1. A

    No

  2. B

    Yes

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Correct answer

  • B

    Yes

Question 2 on its own page

Question 3

+3 marksOne correct option

Let i.i.d. Normal(1, 18). 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
Question 3 on its own page

Question 4

+3 marksWritten answer

Let with PDF . Define a random variable . Find the value of . Enter the answer correct to two decimal places.

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Question 5

+3 marksWritten answer

The joint probability mass function of two discrete random variables and is given by

What is the value of ? Enter the answer correct to two decimal places.

The joint probability mass function of two discrete random variables and is given by
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Question 6

+3 marksWritten answer

A random variable has the moment generating function

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

A random variable has the moment generating function
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Question 6 on its own page

Question 7

+0.5 marksWritten answer
Figure from the original question paper

Enter the correct option number for .

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Question 8

+1 markWritten answer
Figure from the original question paper

Enter the correct option number for .

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Question 9

+0.5 marksWritten answer
Figure from the original question paper

Enter the correct option number for .

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Question 10

+0.5 marksWritten answer
Figure from the original question paper

Enter the correct option number for .

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Question 11

+0.5 marksWritten answer
Figure from the original question paper

Enter the correct option number for .

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Question 12

+2 marksWritten answer

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

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Question 13

+2 marksWritten answer

Let the random variable represent the time (in hours) that a student spends studying for a short quiz.Suppose the PDF of is

Based on the above data, answer the given subquestions.

Let the random variable represent the time (in hours) that a student spends studying for a short quiz.Suppose the PDF o

Find the value of .

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Question 14

+3 marksWritten answer

Let the random variable represent the time (in hours) that a student spends studying for a short quiz.Suppose the PDF of is

Based on the above data, answer the given subquestions.

Let the random variable represent the time (in hours) that a student spends studying for a short quiz.Suppose the PDF o

Find the value of . Enter the answer correct to one decimal place.

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Question 15

+2 marksOne or more correct options

Let be i.i.d. samples with mean and finite variance . Let be the sample mean. Based on the above data, answer the given subquestions.

Which of the following statements is/are correct?

Select all that apply.

  1. A

    The variance of the sample mean is equal to and does not depend on .

  2. B

    The sample mean is a random variable whose value depends on the particular sampling instance.

  3. C

    As increases, the variance of the sample mean decreases, causing the values of to cluster closer to .

  4. D

    The mean is a constant real number and is not a random variable.

Show answer

Correct answers

  • B

    The sample mean is a random variable whose value depends on the particular sampling instance.

  • C

    As increases, the variance of the sample mean decreases, causing the values of to cluster closer to .

  • D

    The mean is a constant real number and is not a random variable.

Question 15 on its own page

Question 16

+3 marksWritten answer

Let be i.i.d. samples with mean and finite variance . Let be the sample mean. Based on the above data, answer the given subquestions.

Using Chebyshev's inequality, find the smallest integer value such that

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Question 16 on its own page

Question 17

+3 marksOne correct option

A hospital is conducting a study on enzyme levels (in units per liter, U/L) in blood in adults aged 30–40. Based on historical data 60% of the participants are healthy and 40% have a mild metabolic disorder. Enzyme levels ( ) in healthy individuals follow Normal(50, 36) and for those with the disorder is Normal(60, 25). Based on the above data, answer the given subquestions.

What is the marginal PDF of at ?

  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
Question 17 on its own page

Question 18

+2 marksOne correct option

A hospital is conducting a study on enzyme levels (in units per liter, U/L) in blood in adults aged 30–40. Based on historical data 60% of the participants are healthy and 40% have a mild metabolic disorder. Enzyme levels ( ) in healthy individuals follow Normal(50, 36) and for those with the disorder is Normal(60, 25). Based on the above data, answer the given subquestions.

A randomly selected patient from this age group is found to have an enzyme level of 50 U/L.What is the probability that the patient is healthy?

  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 18 on its own page

Question 19

+2 marksOne correct option

A factory produces light bulbs whose lifetimes have mean hours and standard deviation hours. A quality inspector randomly selects bulbs and computes the sample mean lifetime. Based on the above data, answer the given subquestions.

Which of the following statements is correct about the distribution of the sample mean?

  1. A

    The distribution of the sample mean is approximately normal with mean and standard deviation .

  2. B

    The distribution of the sample mean is approximately normal with mean and standard deviation .

  3. C

    The distribution of the sample mean is approximately uniform between and .

  4. D

    The Central Limit Theorem cannot be applied since the original distribution is not normal.

Show answer

Correct answer

  • A

    The distribution of the sample mean is approximately normal with mean and standard deviation .

Question 19 on its own page

Question 20

+3 marksWritten answer

A factory produces light bulbs whose lifetimes have mean hours and standard deviation hours. A quality inspector randomly selects bulbs and computes the sample mean lifetime. Based on the above data, answer the given subquestions.

Find the probability that the sample mean lifetime exceeds hours. Enter the answer correct to two decimal places.

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Question 21

+1 markWritten answer
Figure from the original question paper
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Question 22

+1 markWritten answer

Let the random variable represent the time (in hours) that a student spends studying for a short quiz.Suppose the PDF of is

Based on the above data, answer the given subquestions.

Let the random variable represent the time (in hours) that a student spends studying for a short quiz.Suppose the PDF o
Show answer

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Question 22 on its own page

Question 23

+1 markWritten answer

Let be i.i.d. samples with mean and finite variance . Let be the sample mean. Based on the above data, answer the given subquestions.

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Question 23 on its own page

Question 24

+1 markWritten answer

A hospital is conducting a study on enzyme levels (in units per liter, U/L) in blood in adults aged 30–40. Based on historical data 60% of the participants are healthy and 40% have a mild metabolic disorder. Enzyme levels ( ) in healthy individuals follow Normal(50, 36) and for those with the disorder is Normal(60, 25). Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 24 on its own page

Question 25

+1 markWritten answer

A factory produces light bulbs whose lifetimes have mean hours and standard deviation hours. A quality inspector randomly selects bulbs and computes the sample mean lifetime. Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 25 on its own page