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Free IIT Madras BS notes, PYQs and mock tests at btechi.in

Stats II · Joint, marginal & conditional

21 questions · 41 marks · 6 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Statistics for Data Science II

Joint, marginal & conditional

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.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Useful Reference Data for this Paper
Read the passage below, then answer Q1–Q6
Q1NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q2NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q3NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q4NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q5NAT0.5 Marks·Write the number
Key ↓
Your answer:
Q6NAT0.5 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q7–Q8
Based on the above data, answer the given subquestions.
Q7MCQ3 Marks·Choose one option
Key ↓
1. A0.20
2. B0.30
3. C0.45
4. D0.25
Q8NAT2 Marks·Write the number
Key ↓
Your answer:

End Term · 31 Aug 2025 (FN)End Term

Read the passage below, then answer Q9–Q10
Based on the above data, answer the given subquestions.
Q9MCQ2 Marks·Choose one option
Asked 4 times Key ↓
Find the value of k .
1. A17
2. B18
3. C1/17
4. D1/18
Q10NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Useful Reference Data for this Paper
Q11NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q12–Q13
Based on the above data, answer the given subquestions.
Q12MCQ3 Marks·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q13NAT2 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 Q14–Q15
Based on the above data, answer the given subquestions.
Q14MCQ2 Marks·Choose one option
Asked 5 times Key ↓
What is the marginal distribution of Y ?
1. A
2. B
3. C
4. D
Q15NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:

End Term · 13 Apr 2025 (AN)End Term

Read the passage below, then answer Q16–Q17
The joint density function of two continuous random variables X and Y is given as:
Based on the above data, answer the given subquestions.
Q16MCQ2 Marks·Choose one option
Asked 5 times Key ↓
Find the marginal probability density function of X.
1. A
2. B
3. C
4. D
Q17NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Read the passage below, then answer Q18–Q19
Based on the above data, answer the given subquestions.
Q18MCQ2 Marks·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q19MCQ3 Marks·Choose one option
Key ↓
Are X and Y independent?
1. AYes
2. BNo

End Term · 22 Dec 2024 (AN)End Term

Read the passage below, then answer Q20–Q21
Based on the above data, answer the given subquestions.
Q20MCQ2 Marks·Choose one option
Asked 5 times Key ↓
Find the Marginal distribution of X.
1. A
2. B
3. C
4. D
Q21NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q15

Q22

Q38

Q412

Q59

Q610

Q7D

Q80.43 to 0.47

Q9B

Q100.8 to 0.86

Q110.22 to 0.28

Q12D

Q130.29 to 0.35

Q14B

Q150.42 to 0.48

Q16B

Q170.3 to 0.36

Q18B

Q19A

Q20B

Q210.3 to 0.36

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.