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January 2025 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II End Term: 13 April 2025, Set QDD3 (January 2025 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 13 Apr 2025, in the January 2025 term, set QDD3: 15 questions for 40 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
15
Marks
40
Duration
180 min
MCQ
9
MSQ
1
Numerical
5
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION FN EXAM QDF1 13 Apr 2025 · No negative marking.

Question 1

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 1 on its own page

Question 2

+3 marksOne correct option
  1. A

    Gamma (145, 12)

  2. B

    Gamma (12, 145)

  3. C

    Gamma (145, 72)

  4. D

    Gamma (72, 145)

Show answer

Correct answer

  • C

    Gamma (145, 72)

Question 2 on its own page

Question 3

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 3 on its own page

Question 4

+3 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
  5. E
Show answer

Correct answers

  • A
  • C
  • D
Question 4 on its own page

Question 5

+3 marksNumerical answer
Show answer

Correct answer: 0.25 (accepted within ±0.03)

Question 5 on its own page

Question 6

+2 marksOne correct option

The joint density function of two continuous random variables X and Y is given as:

Based on the above data, answer the given subquestions.

Find the marginal probability density function of X.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 6 on its own page

Question 7

+3 marksNumerical answer

The joint density function of two continuous random variables X and Y is given as:

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.33 (accepted within ±0.03)

Question 7 on its own page

Question 8

+2 marksOne correct option

A factory produces electronic processors and their performance score depends on two factors: (i) Number of Cores (X), (ii) Cache Size (Y ). For a randomly chosen processor, the probability mass functions (PMFs) of X and Y are given as follows:

The overall performance score (Z) of a processor is defined as Z= 4X + 3Y .
Based on the above data, answer the given subquestions.

Identify all the possible values of overall performance score (Z).

  1. A

    {10, 13, 14, 16, 17, 20}

  2. B

    {11, 13, 19, 14, 18, 25}

  3. C

    {10, 11, 14, 16, 19, 20}

  4. D

    {11, 14, 15, 18, 19, 22}

Show answer

Correct answer

  • D

    {11, 14, 15, 18, 19, 22}

Question 8 on its own page

Question 9

+3 marksNumerical answer

A factory produces electronic processors and their performance score depends on two factors: (i) Number of Cores (X), (ii) Cache Size (Y ). For a randomly chosen processor, the probability mass functions (PMFs) of X and Y are given as follows:

The overall performance score (Z) of a processor is defined as Z= 4X + 3Y .
Based on the above data, answer the given subquestions.

Compute the value of E [ Z ]. Enter the answer correct to one decimal place.

Show answer

Correct answer: 16.2 (accepted within ±0.2)

Question 9 on its own page

Question 10

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the maximum likelihood estimate of λ for the given sample. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.93 (accepted within ±0.03)

Question 10 on its own page

Question 11

+2 marksOne correct option

Based on the above data, answer the given subquestions.

Assume the prior distribution of λ to be Gamma(2,2). Determine the posterior distribution of λ.

  1. A

    Gamma(7, 7.4)

  2. B

    Gamma(6.4, 7)

  3. C

    Gamma(7, 6.4)

  4. D

    Gamma(7.4, 7)

Show answer

Correct answer

  • A

    Gamma(7, 7.4)

Question 11 on its own page

Question 12

+2 marksOne correct option

Based on the above data, answer the given subquestions.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 12 on its own page

Question 13

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 2.67 (accepted within ±0.03)

Question 13 on its own page

Question 14

+2 marksOne correct option

Based on the above data, answer the given subquestions.

State the null and alternative hypotheses.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • C
Question 14 on its own page

Question 15

+3 marksOne correct option

Based on the above data, answer the given subquestions.

Suppose the researcher decides to increase the sample size 64 to 100 while keeping the same rejection threshold. What will be effect on level of significance?

  1. A

    The significance level will increase from 0.05 to 0.09.

  2. B

    The significance level will be same.

  3. C

    The significance level will decrease from 0.09 to 0.01.

  4. D

    The significance level will decrease from 0.09 to 0.05.

Show answer

Correct answer

  • D

    The significance level will decrease from 0.09 to 0.05.

Question 15 on its own page