Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Statistics for Data Science II
Method of moments & MLE
Examination Instructions & Guidelines
- Solve on notebook/paper first before checking solutions.
- MCQ: Exactly 1 option is correct. Negative marking applies.
- NAT: Numerical response. No negative marking.
- Scientific calculator allowed for all calculations.
- Official answer key is sealed at the end of this sheet.
End Term · 31 Aug 2025 (FN)End Term
- Q1MCQ3 Marks·Choose one option
- A
- B
- C
- D
- A
Read the passage below, then answer Q2–Q3
Based on the above data, answer the given subquestions.
Q2MCQ2 Marks·Choose one optionWhat is the maximum likelihood estimate of θ?
- A
- B
- C
- D
- A
- Q3NAT3 Marks·Write the number
Your answer:
End Term · 13 Apr 2025 (FN)End Term
Read the passage below, then answer Q4–Q5
Based on the above data, answer the given subquestions.
Q4NAT4 Marks·Write the numberFind the method of moments estimate of θ for the given sample.
Your answer:- Q5MCQ1 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 Q6
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.
Q6NAT3 Marks·Write the numberFind the maximum likelihood estimate of λ for the given sample. Enter the answer correct to one decimal place.
Your answer:
End Term · 13 Apr 2025 (AN)End Term
Read the passage below, then answer Q7
Based on the above data, answer the given subquestions.
Q7NAT3 Marks·Write the numberFind the maximum likelihood estimate of λ for the given sample. Enter the answer correct to two decimal places.
Your answer:
End Term · 22 Dec 2024 (FN)End Term
- Q8NAT3 Marks·Write the number
Your answer: Read the passage below, then answer Q9–Q10
Based on the above data, answer the given subquestions.
Q9NAT2 Marks·Write the numberConsider a random sample (1, 0, 1, 2, 2, 0, 1). Find the method of moments estimate of θ for the given sample. Enter the answer correct to two decimal places.
Your answer:- Q10NAT3 Marks·Write the number
Consider a random sample (2, 0, 1, 1, 2, 2, 1, 1, 0, 0). Find the maximum likelihood estimate of θ for the given sample. Enter the answer correct to one decimal place.
Your answer:
End Term · 22 Dec 2024 (AN)End Term
- Q11NAT3 Marks·Write the number
Your answer: Read the passage below, then answer Q12–Q13
Based on the above data, answer the given subquestions.
Q12NAT3 Marks·Write the number
Your answer:- Q13NAT2 Marks·Write the number
Your answer: