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September 2023 term · Statistics for Data Science II · BSMA1004

Stats 2 End Term: 24 December 2023, Set FDF1 (September 2023 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) End Term paper sat on 24 Dec 2023, in the September 2023 term, set FDF1: 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
4
Numerical
8
MSQ
3
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION FN EXAM FDF1 24 Dec 2023 · No negative marking.

Question 1

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

Correct answer

  • B
Question 1 on its own page

Question 2

+3 marksNumerical answer
Show answer

Correct answer: 14

Question 2 on its own page

Question 3

+3 marksNumerical answer
Show answer

Correct answer: 3

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
Show answer

Correct answers

  • B
  • D
Question 4 on its own page

Question 5

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • C
  • D
Question 5 on its own page

Question 6

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Let a random sample of X be 1, 2, 2.5, 2.5, 2. Find the method of moments estimate of α for the given sample.

Show answer

Correct answer: 1

Question 6 on its own page

Question 7

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Let a random sample of X be 6, 7.5, 7.5, 3, 6. Find the maximum likelihood estimate of α for the given sample.

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Correct answer: 3

Question 7 on its own page

Question 8

+3 marksOne or more correct options

Based on the above data, answer the given subquestions.

Which of the following option(s) is (are) true about the moment generating function of the random variable Y ?

Select all that apply.

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

Correct answers

  • A
  • D
Question 8 on its own page

Question 9

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the expected value of Y .

Show answer

Correct answer: 2

Question 9 on its own page

Question 10

+2 marksOne correct option

The battery life of a smartphone is normal with standard deviation of 4 hours. The manufacturer claims that their latest model’s battery life lasts, on average, for 10 hours before needing a recharge. We suspect that this is too low. To investigate this claim, we have selected a random sample of 100 smartphones. If the average battery life of these smartphones is greater than 11.1 hours, the manufacturer’s claim will be rejected; otherwise, it will be accepted.
Based on the above data, answer the given subquestions.

Define null hypothesis and alternative hypothesis.

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

Correct answer

  • A
Question 10 on its own page

Question 11

+3 marksNumerical answer

The battery life of a smartphone is normal with standard deviation of 4 hours. The manufacturer claims that their latest model’s battery life lasts, on average, for 10 hours before needing a recharge. We suspect that this is too low. To investigate this claim, we have selected a random sample of 100 smartphones. If the average battery life of these smartphones is greater than 11.1 hours, the manufacturer’s claim will be rejected; otherwise, it will be accepted.
Based on the above data, answer the given subquestions.

Find the power of the test for μ = 11. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.4 (accepted within ±0.03)

Question 11 on its own page

Question 12

+3 marksOne correct option

Let p be the proportion of customers who favor a newly introduced feature in our mobile app. The product team randomly selected 50 customers and asked them if they appreciate the new feature. From the survey, 20 out of the 50 customers responded with a ‘yes.’
Based on the above data, answer the given subquestions.

Find the posterior distribution of p for a Uniform [0, 1] prior.

  1. A

    Beta(20, 30)

  2. B

    Beta(30, 20)

  3. C

    Beta(21, 31)

  4. D

    Beta(31, 21)

Show answer

Correct answer

  • C

    Beta(21, 31)

Question 12 on its own page

Question 13

+2 marksNumerical answer

Let p be the proportion of customers who favor a newly introduced feature in our mobile app. The product team randomly selected 50 customers and asked them if they appreciate the new feature. From the survey, 20 out of the 50 customers responded with a ‘yes.’
Based on the above data, answer the given subquestions.

Find the posterior mean. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.4 (accepted within ±0.03)

Question 13 on its own page

Question 14

+2 marksOne correct option

Let X represent the time (in hours) it takes for a light bulb to burn out. Assume X follows an exponential distribution with a mean of 100 hours.
Based on the above data, answer the given subquestions.

What is the probability that a randomly selected light bulb will last more than 150 hours?

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

Correct answer

  • B
Question 14 on its own page

Question 15

+3 marksNumerical answer

Let X represent the time (in hours) it takes for a light bulb to burn out. Assume X follows an exponential distribution with a mean of 100 hours.
Based on the above data, answer the given subquestions.

Find P(X > 300 | X > 200). Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.37 (accepted within ±0.03)

Question 15 on its own page