Figure from the original question paper

(B) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the original question paper

(C) Option figure from the original question paper

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the passage in the original paper What is the value of p?

(D) Option figure from the original question paper

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

Figure from the passage in the original paper Based on the above data, answer the given subquestions. What is the CDF of X?

(B) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the passage in the original paper Based on the above data, answer the given subquestions. What is the value of P(−4 \< X ≤ 6)?

(B) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

January 2025 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II Quiz 1: 23 February 2025 (January 2025 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 1 paper sat on 23 Feb 2025, in the January 2025 term: 17 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions: 17
Marks: 40
Duration: 120 min
MCQ: 8
Numerical: 8
MSQ: 1

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M DIPLOMA AN EXAM QDD2 23 Feb 2025 · No negative marking.

Question 1

+3 marksOne correct option

Show answer

Correct answer

Question 1 on its own page

Question 2

+3 marksOne correct option

Show answer

Correct answer

Question 2 on its own page

Question 3

+3 marksNumerical answer

A call center analyst monitors the number of calls received at the centre daily. Let X denote the number of calls received in a day. Using Markov’s inequality, the analyst determines an upper bound of 0.48 on the probability of receiving more than 249 calls. Calculate the mean of X.

Show answer

Correct answer: 120

Question 3 on its own page

Question 4

+3 marksNumerical answer

Show answer

Correct answer: 0.5

Question 4 on its own page

Question 5

+1 markOne correct option

What is the value of p?

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Correct answer

Question 5 on its own page

Question 6

+2 marksNumerical answer

Find the expected amount of money to be gain. Enter the answer correct to two decimal places.

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Correct answer: 13.75 (accepted within ±0.03)

Question 6 on its own page

Question 7

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Find Var(W). Enter the answer correct to two decimal places.

Show answer

Correct answer: 2.92 (accepted within ±0.03)

Question 7 on its own page

Question 8

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

What is the value of E(Z +W)? Enter the answer correct to two decimal places.

Show answer

Correct answer: 9.75 (accepted within ±0.03)

Question 8 on its own page

Question 9

+3 marksOne correct option

Based on the above data, answer the given subquestions.

Identify the correct joint PMF table of X and Y .

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Correct answer

Question 9 on its own page

Question 10

+2 marksOne correct option

Based on the above data, answer the given subquestions.

What is the marginal distribution of X?

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Correct answer

Question 10 on its own page

Question 11

+3 marksOne correct option

Let X and Y denote the number of customers arriving at two different service counters (Counter 1 and Counter 2) in a bank during a one-hour interval. The random variables X and Y follow Poisson distributions with mean arrival rates of 15 customers per hour at Counter 1 and 25 customers per hour at Counter 2, respectively. Assume that X and Y are independent.
Based on the above data, answer the given subquestions.

If Z represents the combined total number of customers arriving at both counters during a one- hour interval, then determine the PMF of Z.

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Correct answer

Question 11 on its own page

Question 12

+2 marksOne or more correct options

Which of the following option(s) is/are correct?

Select all that apply.

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Correct answers

Question 12 on its own page

Question 13

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Find the value of a.

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Correct answer: 3

Question 13 on its own page

Question 14

+2 marksOne correct option

Based on the above data, answer the given subquestions.

What is the CDF of X?

Show answer

Correct answer

Question 14 on its own page

Question 15

+2 marksOne correct option

Based on the above data, answer the given subquestions.

What is the value of P(−4 < X ≤ 6)?

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Correct answer

Question 15 on its own page

Question 16

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the probability that the factory will produce at most 3 defective light bulbs in a batch of 5 light bulbs. Enter the answer correct to two decimal places.

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Correct answer: 0.93 (accepted within ±0.03)

Question 16 on its own page

Question 17

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the value of P(X ≤ 4 | X > 1).

Show answer

Correct answer: 1

Question 17 on its own page