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September 2025 term · Statistics for Data Science I · BSMA1002

Statistics for Data Science I End Term: 21 December 2025 (September 2025 term)

The IIT Madras BS Statistics for Data Science I (Stats 1) End Term paper sat on 21 Dec 2025, in the September 2025 term: 16 questions for 42 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
16
Marks
42
Duration
180 min
Written
11
MCQ
4
MSQ
1
Take as mock testPractise with answers

Updated

Official paper: Statistics1 18 Dec 25 · No negative marking.

Question 1

+3 marksWritten answer

Suppose that a continuous random variable is uniformly distributed between and . The value of mean and variance of are 9 and 3 respectively. Based on the above data, answer the given subquestions.

Find the value of .

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Question 2

+2 marksWritten answer

Suppose that a continuous random variable is uniformly distributed between and . The value of mean and variance of are 9 and 3 respectively. Based on the above data, answer the given subquestions.

Find the value of . Enter the answer correct to two decimal place.

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Question 3

+3 marksWritten answer

The number of customer arriving at a bank counter follows a Poisson distribution with an average of 4 arrivals per hour. What is the probability that at least 2 customers arrives in 30 minutes? Enter the answer correct to two decimal places.

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Question 4

+4 marksWritten answer

The probability mass function of a discrete random variable X is given by

Find the value of such that . Enter the answer correct to one decimal place.

The probability mass function of a discrete random variable X is given by
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Question 4 on its own page

Question 5

+3 marksWritten answer

A random variable represents the number of packages delivered by a courier company in a day. The cumulative distribution function (CDF) of X is given below:

Find the value of . Enter the answer correct to two decimal places.

A random variable represents the number of packages delivered by a courier company in a day. The cumulative distributio
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Question 5 on its own page

Question 6

+3 marksOne correct option

Suppose is a binomial random variable with parameters and

. Define a new random variable . Based on the above data, answer the given subquestions.

Suppose is a binomial random variable with parameters and

Find the PMF of .

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
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Correct answer

  • A
    Figure from the original question paper
Question 6 on its own page

Question 7

+3 marksWritten answer

Suppose is a binomial random variable with parameters and

. Define a new random variable . Based on the above data, answer the given subquestions.

Suppose is a binomial random variable with parameters and

Find the expected value of .

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Question 8

+3 marksOne correct option

A box contains 3 red balls and 3 blue balls. A student randomly picks 3 balls without replacement. Let be the random variable representing the number of red balls selected. Which of the following option is correct?

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

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Correct answer

  • D

    —

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Question 9

+2 marksWritten answer

Consider the dataset 4, 7, 5, 3, 9. If 3 is added to all observations, what is the percentile of the new dataset?

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Question 10

+4 marksOne correct option

Based on the information given in Table 3, choose the correct option regarding the correlation coefficient between hours studied and test scores of five students.

Based on the information given in Table 3, choose the correct option regarding the correlation coefficient between hour
  1. A

    The value of is 0.65 and shows a moderate positive correlation.

  2. B

    The value of is 0.87 and shows a strong positive correlation.

  3. C

    The value of is 0.92 and shows a very strong positive correlation.

  4. D

    The value of is -0.80 and shows a very strong negative correlation.

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Correct answer

  • B

    The value of is 0.87 and shows a strong positive correlation.

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Question 11

+2 marksOne or more correct options

Which of the following options is(are) correct?

Select all that apply.

  1. A

    The variable height of students is measured on an interval scale.

  2. B

    The average temperature recorded each day for one week is time-series data.

  3. C

    Cross-sectional data are collected at a single point in time across several individuals, firms, or regions etc.

  4. D

    The brand of smartphone a person uses is a qualitative variable.

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Correct answers

  • B

    The average temperature recorded each day for one week is time-series data.

  • C

    Cross-sectional data are collected at a single point in time across several individuals, firms, or regions etc.

  • D

    The brand of smartphone a person uses is a qualitative variable.

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Question 12

+3 marksWritten answer

At a seminar, there are 30 participants, consisting of 20 men and 10 women. • Each man shakes hands only with other men. • Each woman shakes hands only with other women. If every allowed pair of people has exactly one handshake, find the total number of handshakes that occur at the seminar.

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Question 13

+3 marksOne correct option

There are two bags, Bag A and Bag B. Bag A contains 2 red balls and 1 blue ball, while Bag B contains 1 red ball and 2 blue balls. The probability of choosing Bag A is , and the probability of choosing Bag B is . After selecting a bag, one ball is drawn from it. What is the probability that the ball drawn is red?

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

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Correct answer

  • B

    —

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Question 14

+2 marksWritten answer

The median of the data set is . What is the median of the transformed dataset ?

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Question 15

+1 markWritten answer

Suppose that a continuous random variable is uniformly distributed between and . The value of mean and variance of are 9 and 3 respectively. Based on the above data, answer the given subquestions.

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Question 16

+1 markWritten answer

Suppose is a binomial random variable with parameters and

. Define a new random variable . Based on the above data, answer the given subquestions.

Suppose is a binomial random variable with parameters and
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Question 16 on its own page