Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Statistics for Data Science II
End Term · 13 Apr 2025 (Forenoon)
Examination Instructions & Guidelines
- Solve on notebook/paper first before checking solutions.
- MCQ: Exactly 1 option is correct. Negative marking applies.
- MSQ: One or more options correct. Select all to score.
- NAT: Numerical response. No negative marking.
- Scientific calculator allowed for all calculations.
- Official answer key is sealed at the end of this sheet.
- Q1MCQ3 Marks·Choose one option
- A
- B
- C
- D
- A
- Q2MCQ3 Marks·Choose one option
- A
- B
- C
- D
- A
- Q3MSQ3 Marks·Choose all correct options
- A
- B
- C
- D
- E
- A
- Q4NAT3 Marks·Write the number
Your answer: Read the passage below, then answer Q5–Q6
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.
Q5MCQ2 Marks·Choose one optionThe 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.
- A
- B
- C
- D
- A
- Q6MCQ1 Mark·Choose one option
Using the prior distribution and the observed data, compute the posterior distribution of p.
- ABeta(50.4, 154.6)
- BBeta(1.4, 5.6)
- CBeta(5.6, 1.4)
- DBeta(51.4, 155.6)
Read the passage below, then answer Q7–Q8
Based on the above data, answer the given subquestions.
Q7NAT4 Marks·Write the numberFind the method of moments estimate of θ for the given sample.
Your answer:- Q8MCQ1 Mark·Choose one option
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.
- AThe company meets the requirement.
- BThe company does not meet the requirement.
Read the passage below, then answer Q9–Q10
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.
Q9NAT3 Marks·Write the numberFind the maximum likelihood estimate of λ for the given sample. Enter the answer correct to one decimal place.
Your answer:- Q10MCQ2 Marks·Choose one option
Assume the prior distribution of λ to be Gamma(3, 2). Determine the posterior distribution of λ.
- AGamma(45, 12)
- BGamma(12, 46)
- CGamma(46, 12)
- DGamma(12, 45)
Read the passage below, then answer Q11–Q12
Based on the above data, answer the given subquestions.
Q11NAT3 Marks·Write the number
Your answer:- Q12NAT2 Marks·Write the number
Your answer: Read the passage below, then answer Q13–Q14
Based on the above data, answer the given subquestions.
Q13NAT3 Marks·Write the number
Your answer:- Q14MCQ2 Marks·Choose one option
- A16
- B18.8
- C6
- D2.8
Read the passage below, then answer Q15–Q17
Based on the above data, answer the given subquestions.
Q15NAT1 Mark·Write the number
Your answer:- Q16MCQ2 Marks·Choose one option
- A
- B
- C
- D
- A
- Q17NAT2 Marks·Write the number
Your answer: