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Stats II · Bayesian estimation

14 questions · 33 marks · 5 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Statistics for Data Science II

Bayesian estimation

Official Paper

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
Asked 4 times Key ↓
1. ABeta (29, 44)
2. BBeta (30, 45)
3. CBeta (20, 30)
4. DBeta (10, 15)
Read the passage below, then answer Q2–Q3
Based on the above data, answer the given subquestions.
Q2MCQ3 Marks·Choose one option
Key ↓
Find the posterior distribution of θ.
1. A
2. B
3. C
4. D
Q3NAT2 Marks·Write the number
Asked 2 times Key ↓
If the posterior mean is 0.6, then find the value of m.
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Read the passage below, then answer Q4–Q5
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.
Q4MCQ2 Marks·Choose one option
Asked 2 times Key ↓
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
Q5MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Using the prior distribution and the observed data, compute the posterior distribution of p.
1. ABeta(50.4, 154.6)
2. BBeta(1.4, 5.6)
3. CBeta(5.6, 1.4)
4. DBeta(51.4, 155.6)
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.
Q6MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Assume the prior distribution of λ to be Gamma(3, 2). Determine the posterior distribution of λ.
1. AGamma(45, 12)
2. BGamma(12, 46)
3. CGamma(46, 12)
4. DGamma(12, 45)

End Term · 13 Apr 2025 (AN)End Term

Q7MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. AGamma (145, 12)
2. BGamma (12, 145)
3. CGamma (145, 72)
4. DGamma (72, 145)
Read the passage below, then answer Q8
Based on the above data, answer the given subquestions.
Q8MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Assume the prior distribution of λ to be Gamma(2,2). Determine the posterior distribution of λ.
1. AGamma(7, 7.4)
2. BGamma(6.4, 7)
3. CGamma(7, 6.4)
4. DGamma(7.4, 7)
Read the passage below, then answer Q9–Q10
Based on the above data, answer the given subquestions.
Q9MCQ2 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q10NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Read the passage below, then answer Q11–Q12
A company is testing a new AI-based chatbot for customer service and wants to know if it is liked by its users. Let p be the true proportion of users who would find the chatbot helpful. The team selected 30 customers randomly and asked if they found the chatbot useful. Out of these, 12 responded ‘yes’.
Based on the above data, answer the given subquestions.
Q11MCQ3 Marks·Choose one option
Asked 4 times Key ↓
Find the posterior distribution of p for a Beta [3, 2] prior.
1. ABeta(12, 18)
2. BBeta(15, 20)
3. CBeta(14, 19)
4. DBeta(20, 15)
Q12NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the posterior mean using the correct prior from the previous question. Enter the answer correct to two decimal places.
Your answer:

End Term · 22 Dec 2024 (AN)End Term

Read the passage below, then answer Q13–Q14
Let p be the true 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.
Q13MCQ3 Marks·Choose one option
Asked 4 times Key ↓
Find the posterior distribution of p for a Uniform [0, 1] prior.
1. ABeta(20, 30)
2. BBeta(30, 20)
3. CBeta(21, 31)
4. DBeta(31, 21)
Q14NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the posterior mean. Enter the answer correct to two decimal places.
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q1B

Q2D

Q32

Q4C

Q5D

Q6C

Q7C

Q8A

Q9A

Q102.64 to 2.7

Q11B

Q120.4 to 0.46

Q13C

Q140.37 to 0.43

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.