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January 2025 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II End Term: 13 April 2025, Set QDF1 (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 QDF1: 17 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
17
Marks
40
Duration
180 min
MCQ
8
MSQ
1
Numerical
8
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
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 2 on its own page

Question 3

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • B
  • C
  • E
Question 3 on its own page

Question 4

+3 marksNumerical answer
Show answer

Correct answer: 21.65 (accepted within ±0.03)

Question 4 on its own page

Question 5

+2 marksOne correct option

A software company is analyzing the bug reports for their newly developed application. Some bug reports identify a critical bug in the application. To estimate the probability p of a bug report identifying a critical bug, they collect a random sample of 200 bug reports, and find that 50 are classified as critical. The company adopts a Bayesian approach with a Beta distribution as the prior for p.
Based on the above data, answer the given subquestions.

The company assumes a Beta(1.4, b) prior for p. Given that prior knowledge suggests the expected value of p is approximately 0.2, determine the appropriate value of b.

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

Correct answer

  • C
Question 5 on its own page

Question 6

+1 markOne correct option

A software company is analyzing the bug reports for their newly developed application. Some bug reports identify a critical bug in the application. To estimate the probability p of a bug report identifying a critical bug, they collect a random sample of 200 bug reports, and find that 50 are classified as critical. The company adopts a Bayesian approach with a Beta distribution as the prior for p.
Based on the above data, answer the given subquestions.

Using the prior distribution and the observed data, compute the posterior distribution of p.

  1. A

    Beta(50.4, 154.6)

  2. B

    Beta(1.4, 5.6)

  3. C

    Beta(5.6, 1.4)

  4. D

    Beta(51.4, 155.6)

Show answer

Correct answer

  • D

    Beta(51.4, 155.6)

Question 6 on its own page

Question 7

+4 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the method of moments estimate of θ for the given sample.

Show answer

Correct answer: 4

Question 7 on its own page

Question 8

+1 markOne correct option

Based on the above data, answer the given subquestions.

The company has a policy requirement that the average waiting time must not exceed 3 minutes. Based on the estimated value of θ, determine whether the company meets this requirement.

  1. A

    The company meets the requirement.

  2. B

    The company does not meet the requirement.

Show answer

Correct answer

  • A

    The company meets the requirement.

Question 8 on its own page

Question 9

+3 marksNumerical answer

A research team is analyzing customer complaints per day for a new service. The number of complaints X follows a Poisson distribution with an unknown average rate λ. The number of complaints observed over a period of 10 days are as follows :
3, 5, 2, 4, 6, 3, 4, 7, 5, 4
The team aims to estimate λ using two different methods: Maximum Likelihood Estimation (MLE) and Bayesian Estimation.
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 one decimal place.

Show answer

Correct answer: 4.3 (accepted within ±0.2)

Question 9 on its own page

Question 10

+2 marksOne correct option

A research team is analyzing customer complaints per day for a new service. The number of complaints X follows a Poisson distribution with an unknown average rate λ. The number of complaints observed over a period of 10 days are as follows :
3, 5, 2, 4, 6, 3, 4, 7, 5, 4
The team aims to estimate λ using two different methods: Maximum Likelihood Estimation (MLE) and Bayesian Estimation.
Based on the above data, answer the given subquestions.

Assume the prior distribution of λ to be Gamma(3, 2). Determine the posterior distribution of λ.

  1. A

    Gamma(45, 12)

  2. B

    Gamma(12, 46)

  3. C

    Gamma(46, 12)

  4. D

    Gamma(12, 45)

Show answer

Correct answer

  • C

    Gamma(46, 12)

Question 10 on its own page

Question 11

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.09 (accepted within ±0.03)

Question 11 on its own page

Question 12

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.975 (accepted within ±0.025)

Question 12 on its own page

Question 13

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 6

Question 13 on its own page

Question 14

+2 marksOne correct option

Based on the above data, answer the given subquestions.

  1. A

    16

  2. B

    18.8

  3. C

    6

  4. D

    2.8

Show answer

Correct answer

  • D

    2.8

Question 14 on its own page

Question 15

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 3

Question 15 on its own page

Question 16

+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

  • B
Question 16 on its own page

Question 17

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.117 (accepted within ±0.003)

Question 17 on its own page