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Stats II · All 2025 papers

88 questions · 200 marks · 5 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Statistics for Data Science II

All 2025 papers

Official Paper

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.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Useful Reference Data for this Paper
Q1MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q2NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q3NAT3 Marks·Write the number
Key ↓
Your answer:
Q4NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q5–Q10
Q5NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q6NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q7NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q8NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q9NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q10NAT0.5 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q11–Q12
Based on the above data, answer the given subquestions.
Q11MCQ2 Marks·Choose one option
Asked 4 times Key ↓
Find the value of k.
1. A
2. B
3. C
4. D
Q12NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q13–Q14
Based on the above data, answer the given subquestions.
Q13MCQ3 Marks·Choose one option
Key ↓
1. A0.20
2. B0.30
3. C0.45
4. D0.25
Q14NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q15–Q16
Based on the above data, answer the given subquestions.
Q15MCQ2 Marks·Choose one option
Key ↓
Using Markov’s inequality, find an upper bound on the probability that the processing time is at least 1.3 times its expected value.
1. A
2. B
3. C
4. D
Q16NAT3 Marks·Write the number
Asked 2 times Key ↓
Using Chebyshev’s inequality, find a lower bound on the probability that the processing time lies between 480 milliseconds and 520 milliseconds. Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q17–Q18
Based on the above data, answer the given subquestions.
Q17MCQ2 Marks·Choose one option
Key ↓
What is the range of Y ?
1. A{0, 1, 2, 3, 4, 5, 6}
2. B{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
3. C{1, 2, 3, 4, 5, 6 }
4. D{ 2, 3, 4, 5, 6, 7, 8, 9}
Q18NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q19–Q20
Based on the above data, answer the given subquestions.
Q19NAT3 Marks·Write the number
Key ↓
Your answer:
Q20MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D

End Term · 31 Aug 2025 (FN)End Term

Q21MCQ3 Marks·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q22MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. ABeta (29, 44)
2. BBeta (30, 45)
3. CBeta (20, 30)
4. DBeta (10, 15)
Q23NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q24–Q29
Q24NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q25NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q26NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q27NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q28NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q29NAT0.5 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q30–Q31
Based on the above data, answer the given subquestions.
Q30MCQ1 Mark·Choose one option
Key ↓
Identify the correct PMF of X.
1. A
2. B
3. C
4. D
Q31NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q32–Q33
Based on the above data, answer the given subquestions.
Q32MCQ2 Marks·Choose one option
Asked 4 times Key ↓
What is the maximum likelihood estimate of θ?
1. A
2. B
3. C
4. D
Q33NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q34–Q35
A tech company claims that the average time their employees take to solve a debugging task is 45 minutes, with a known standard deviation of 10 minutes. A skeptical manager believes this time is too high and takes a random sample of 64 tasks. The manager decides to reject the company’s claim if the sample average time is less than ‘c’ minutes. Based on the given information, answer the subquestions.
Q34MCQ2 Marks·Choose one option
Asked 4 times Key ↓
Define null and alternative hypotheses.
1. A
2. B
3. C
4. D
Q35NAT3 Marks·Write the number
Asked 3 times Key ↓
If the value of the significance level is 0.16, then find the value of ‘c’. Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q36–Q37
Based on the above data, answer the given subquestions.
Q36NAT2 Marks·Write the number
Key ↓
What is the expected number of calls handled by the agent in an hour? Enter the answer correct to one decimal place.
Your answer:
Q37NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q38–Q39
Based on the above data, answer the given subquestions.
Q38MCQ3 Marks·Choose one option
Key ↓
Find the posterior distribution of θ.
1. A
2. B
3. C
4. D
Q39NAT2 Marks·Write the number
Asked 2 times Key ↓
If the posterior mean is 0.6, then find the value of m.
Your answer:
Read the passage below, then answer Q40–Q41
Based on the above data, answer the given subquestions.
Q40MCQ2 Marks·Choose one option
Asked 4 times Key ↓
Find the value of k .
1. A17
2. B18
3. C1/17
4. D1/18
Q41NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Useful Reference Data for this Paper
Q42MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q43MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
5. E
Q44MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q45NAT3 Marks·Write the number
Key ↓
Your answer:
Q46NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q47–Q48
Based on the above data, answer the given subquestions.
Q47MCQ3 Marks·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q48NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the value of P(X < 1, Y < 1). Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q49–Q50
Based on the above data, answer the given subquestions.
Q49MCQ2 Marks·Choose one option
Asked 5 times Key ↓
What is the marginal distribution of Y ?
1. A
2. B
3. C
4. D
Q50NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q51–Q52
Based on the above data, answer the given subquestions.
Q51MCQ3 Marks·Choose one option
Key ↓
Which of the following options is an acceptable approximate model for Y as per the Central Limit Theorem?
1. A
2. B
3. C
4. D
5. E
Q52NAT2 Marks·Write the number
Key ↓
Using the Central Limit Theorem, it is calculated that the approximate value of P(Y > a) is 0.023. What is the value of a? (See the “Useful Data” given in the Question 2 ).
Your answer:
Read the passage below, then answer Q53–Q54
Based on the above data, answer the given subquestions.
Q53NAT3 Marks·Write the number
Key ↓
Your answer:
Q54NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q55–Q56
Based on the above data, answer the given subquestions.
Q55NAT2 Marks·Write the number
Asked 4 times Key ↓
Find the value of k.
Your answer:
Q56NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q57MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q58MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q59MSQ3 Marks·Choose all correct options
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
5. E
Q60NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q61–Q62
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.
Q61MCQ2 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
Q62MCQ1 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 Q63–Q64
Based on the above data, answer the given subquestions.
Q63NAT4 Marks·Write the number
Asked 5 times Key ↓
Find the method of moments estimate of θ for the given sample.
Your answer:
Q64MCQ1 Mark·Choose one option
Key ↓
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. AThe company meets the requirement.
2. BThe company does not meet the requirement.
Read the passage below, then answer Q65–Q66
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.
Q65NAT3 Marks·Write the number
Asked 2 times Key ↓
Find the maximum likelihood estimate of λ for the given sample. Enter the answer correct to one decimal place.
Your answer:
Q66MCQ2 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)
Read the passage below, then answer Q67–Q68
Based on the above data, answer the given subquestions.
Q67NAT3 Marks·Write the number
Key ↓
Your answer:
Q68NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q69–Q70
Based on the above data, answer the given subquestions.
Q69NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q70MCQ2 Marks·Choose one option
Key ↓
1. A16
2. B18.8
3. C6
4. D2.8
Read the passage below, then answer Q71–Q73
Based on the above data, answer the given subquestions.
Q71NAT1 Mark·Write the number
Asked 4 times Key ↓
Your answer:
Q72MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q73NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 13 Apr 2025 (AN)End Term

Q74MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q75MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. AGamma (145, 12)
2. BGamma (12, 145)
3. CGamma (145, 72)
4. DGamma (72, 145)
Q76MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q77MSQ3 Marks·Choose all correct options
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
5. E
Q78NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q79–Q80
The joint density function of two continuous random variables X and Y is given as:
Based on the above data, answer the given subquestions.
Q79MCQ2 Marks·Choose one option
Asked 5 times Key ↓
Find the marginal probability density function of X.
1. A
2. B
3. C
4. D
Q80NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q81–Q82
A factory produces electronic processors and their performance score depends on two factors: (i) Number of Cores (X), (ii) Cache Size (Y ). For a randomly chosen processor, the probability mass functions (PMFs) of X and Y are given as follows:
The overall performance score (Z) of a processor is defined as Z= 4X + 3Y .
Based on the above data, answer the given subquestions.
Q81MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Identify all the possible values of overall performance score (Z).
1. A{10, 13, 14, 16, 17, 20}
2. B{11, 13, 19, 14, 18, 25}
3. C{10, 11, 14, 16, 19, 20}
4. D{11, 14, 15, 18, 19, 22}
Q82NAT3 Marks·Write the number
Asked 3 times Key ↓
Compute the value of E [ Z ]. Enter the answer correct to one decimal place.
Your answer:
Read the passage below, then answer Q83–Q84
Based on the above data, answer the given subquestions.
Q83NAT3 Marks·Write the number
Asked 2 times Key ↓
Find the maximum likelihood estimate of λ for the given sample. Enter the answer correct to two decimal places.
Your answer:
Q84MCQ2 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 Q85–Q86
Based on the above data, answer the given subquestions.
Q85MCQ2 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q86NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q87–Q88
Based on the above data, answer the given subquestions.
Q87MCQ2 Marks·Choose one option
Asked 4 times Key ↓
State the null and alternative hypotheses.
1. A
2. B
3. C
4. D
Q88MCQ3 Marks·Choose one option
Key ↓
Suppose the researcher decides to increase the sample size 64 to 100 while keeping the same rejection threshold. What will be effect on level of significance?
1. AThe significance level will increase from 0.05 to 0.09.
2. BThe significance level will be same.
3. CThe significance level will decrease from 0.09 to 0.01.
4. DThe significance level will decrease from 0.09 to 0.05.

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1D

Q2638

Q30.7

Q40.1

Q55

Q62

Q78

Q812

Q99

Q1010

Q11B

Q120.6 to 0.66

Q13D

Q140.43 to 0.47

Q15B

Q160.73 to 0.77

Q17A

Q180.2 to 0.22

Q191

Q20B

Q21A

Q22B

Q230.01 to 0.03

Q2412

Q251

Q264

Q276

Q289

Q2921.62 to 21.68

Q30D

Q311

Q32B

Q331.185 to 1.191

Q34B

Q3543.73 to 43.79

Q361.4

Q370.7

Q38D

Q392

Q40B

Q410.8 to 0.86

Q42D

Q43A, E

Q44B, D

Q45504

Q460.22 to 0.28

Q47D

Q480.29 to 0.35

Q49B

Q500.42 to 0.48

Q51C

Q52220

Q5360

Q540.75 to 0.81

Q554

Q560.41 to 0.47

Q57A

Q58A

Q59B, C, E

Q6021.62 to 21.68

Q61C

Q62D

Q634

Q64A

Q654.1 to 4.5

Q66C

Q670.06 to 0.12

Q680.95 to 1

Q696

Q70D

Q713

Q72B

Q730.114 to 0.12

Q74A

Q75C

Q76D

Q77A, C, D

Q780.22 to 0.28

Q79B

Q800.3 to 0.36

Q81D

Q8216 to 16.4

Q830.9 to 0.96

Q84A

Q85A

Q862.64 to 2.7

Q87C

Q88D

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.