Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Statistics for Data Science II
End Term · 13 Apr 2025 (Afternoon)
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
- AGamma (145, 12)
- BGamma (12, 145)
- CGamma (145, 72)
- DGamma (72, 145)
- Q3MCQ3 Marks·Choose one option
- A
- B
- C
- D
- A
- Q4MSQ3 Marks·Choose all correct options
- A
- B
- C
- D
- E
- A
- Q5NAT3 Marks·Write the number
Your answer: Read the passage below, then answer Q6–Q7
The joint density function of two continuous random variables X and Y is given as:
Based on the above data, answer the given subquestions.
Q6MCQ2 Marks·Choose one optionFind the marginal probability density function of X.
- A
- B
- C
- D
- A
- Q7NAT3 Marks·Write the number
Your answer: Read the passage below, then answer Q8–Q9
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.
Q8MCQ2 Marks·Choose one optionIdentify all the possible values of overall performance score (Z).
- A{10, 13, 14, 16, 17, 20}
- B{11, 13, 19, 14, 18, 25}
- C{10, 11, 14, 16, 19, 20}
- D{11, 14, 15, 18, 19, 22}
- Q9NAT3 Marks·Write the number
Compute the value of E [ Z ]. Enter the answer correct to one decimal place.
Your answer: Read the passage below, then answer Q10–Q11
Based on the above data, answer the given subquestions.
Q10NAT3 Marks·Write the numberFind the maximum likelihood estimate of λ for the given sample. Enter the answer correct to two decimal places.
Your answer:- Q11MCQ2 Marks·Choose one option
Assume the prior distribution of λ to be Gamma(2,2). Determine the posterior distribution of λ.
- AGamma(7, 7.4)
- BGamma(6.4, 7)
- CGamma(7, 6.4)
- DGamma(7.4, 7)
Read the passage below, then answer Q12–Q13
Based on the above data, answer the given subquestions.
Q12MCQ2 Marks·Choose one option
- A
- B
- C
- D
- A
- Q13NAT3 Marks·Write the number
Your answer: Read the passage below, then answer Q14–Q15
Based on the above data, answer the given subquestions.
Q14MCQ2 Marks·Choose one optionState the null and alternative hypotheses.
- A
- B
- C
- D
- A
- Q15MCQ3 Marks·Choose one option
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?
- AThe significance level will increase from 0.05 to 0.09.
- BThe significance level will be same.
- CThe significance level will decrease from 0.09 to 0.01.
- DThe significance level will decrease from 0.09 to 0.05.