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Stats II · Inequalities, MGF & CLT

7 questions · 18 marks · 2 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Statistics for Data Science II

Inequalities, MGF & CLT

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
Read the passage below, then answer Q1–Q2
Based on the above data, answer the given subquestions.
Q1MCQ2 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
Q2NAT3 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:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Useful Reference Data for this Paper
Q3MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
5. E
Read the passage below, then answer Q4–Q5
Based on the above data, answer the given subquestions.
Q4MCQ3 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
Q5NAT2 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 Q6–Q7
Based on the above data, answer the given subquestions.
Q6NAT3 Marks·Write the number
Key ↓
Your answer:
Q7NAT2 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

Q1B

Q20.73 to 0.77

Q3A, E

Q4C

Q5220

Q660

Q70.75 to 0.81

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.