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January 2022 term · Statistics for Data Science II · BSMA1004

Stats 2 Quiz 1: 30 January 2022, Set QPB1 (January 2022 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 1 paper sat on 30 Jan 2022, in the January 2022 term, set QPB1: 23 questions for 50 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
23
Marks
50
Duration
120 min
Numerical
8
Written
5
MSQ
3
MCQ
7
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION QUIZ EXAM QPB2 30 Jan 2022 · No negative marking.

Question 1

+2 marksNumerical answer

Answer the subquestions.

Suppose X is a continuous random variable uniformly distributed between −1 and 1. Let Y be another random variable such that Y = X². Calculate Cov[X, Y ].

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Correct answer: 0

Question 1 on its own pageAlso asked in Quiz 1 30 Jan 2022

Question 2

+0 marksWritten answer

Answer the subquestions.

Select three facts/formulae/steps from the list of options that you will use for solving previous question.
Note: "This question is optional. We will check your answer to this question if you make a mistake in the previous one. Please enter your answers in comma-separated format. E.g. 1,2,3". Check the list of options given in the data attachment.

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Correct answer: 3, 5, 8, 16

Question 2 on its own page

Question 3

+2 marksOne or more correct options

Use the following information to answer the subquestions

Which of the following options are true?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
  5. E
  6. F
Show answer

Correct answers

  • B
  • E
Question 3 on its own page

Question 4

+3 marksNumerical answer

Use the following information to answer the subquestions

Find the value of P(X1 = 0 | Y = 8). Enter the answer correct to one decimal place.

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Correct answer: 0.2

Question 4 on its own page

Question 5

+0 marksWritten answer

Use the following information to answer the subquestions

Select three facts/formulae/steps from the list of options that you will use for solving previous questions no 5 & 6.
Note: "This question is optional. We will check your answer to this question if you make a mistake in the previous one. Please enter your answers in comma-separated format. E.g. 1,2,3". Check the list of options given in the data attachment.

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Correct answer: 2, 4, 9, 12, 17, 22

Question 5 on its own page

Question 6

+3 marksOne correct option

Use the following information to answer the subquestions

Find the joint PMF of X1 and X2.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • C
Question 6 on its own page

Question 7

+2 marksNumerical answer

Use the following information to answer the subquestions

Find the probability that Kasparov loses the second game. Enter the answer correct to two decimal places.

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Correct answer: 0.68

Question 7 on its own page

Question 8

+1 markOne correct option

Use the following information to answer the subquestions

Which of the following is true about Y ?

  1. A

    Y is a monotonically increasing function of X.

  2. B

    Y is a monotonically decreasing function of X.

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Correct answer

  • A

    Y is a monotonically increasing function of X.

Question 8 on its own page

Question 9

+2 marksOne correct option

Use the following information to answer the subquestions

Find the support of Y .

  1. A
  2. B
  3. C
  4. D
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Correct answer

  • B
Question 9 on its own page

Question 10

+4 marksOne correct option

Use the following information to answer the subquestions

Find the distribution of Y .

  1. A
  2. B
  3. C
  4. D
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Correct answer

  • B
Question 10 on its own page

Question 11

+2 marksOne or more correct options

Use the following information to answer the subquestions

Choose the correct options from the following:

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
Question 11 on its own page

Question 12

+3 marksOne correct option

Use the following information to answer the subquestions

Find the marginal distributions of X and Y .

  1. A
  2. B
  3. C
  4. D
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Correct answer

  • C
Question 12 on its own page

Question 13

+3 marksNumerical answer

Use the following information to answer the subquestions

Find P(X = 3, Y = 3). (Enter the answer correct to three decimal places)

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Correct answer: 0.027 (accepted within ±0.004)

Question 13 on its own page

Question 14

+3 marksNumerical answer

Answer the subquestions.

The time of an interview follows an exponential distribution with an average time of 20 minutes. Find the probability that the interview lasted more than 15 minutes given that it was between 12 and 18 minutes. (Enter the answer correct to two decimal places)

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Correct answer: 0.46 (accepted within ±0.01)

Question 14 on its own page

Question 15

+0 marksWritten answer

Answer the subquestions.

Select three facts/formulae/steps from the list of options that you will use for solving previous question.
Note: "This question is optional. We will check your answer to this question if you make a mistake in the previous one. Please enter your answers in comma-separated format. E.g. 1,2,3". Check the list of options given in the data attachment.

Show answer

Correct answer: 4, 11, 15, 20, 21

Question 15 on its own page

Question 16

+3 marksNumerical answer

Answer the subquestions.

Show answer

Correct answer: 0.25

Question 16 on its own page

Question 17

+0 marksWritten answer

Answer the subquestions.

Select three facts/formulae/steps from the list of options that you will use for solving previous question.
Note: "This question is optional. We will check your answer to this question if you make a mistake in the previous one. Please enter your answers in comma-separated format. E.g. 1,2,3". Check the list of options given in the data attachment.

Show answer

Correct answer: 6, 7, 10, 12, 14, 18

Question 17 on its own page

Question 18

+4 marksNumerical answer

Answer the subquestions.

Show answer

Correct answer: 0.72

Question 18 on its own page

Question 19

+0 marksWritten answer

Answer the subquestions.

Select three facts/formulae/steps from the list of options that you will use for solving previous question.
Note: "This question is optional. We will check your answer to this question if you make a mistake in the previous one. Please enter your answers in comma-separated format. E.g. 1,2,3". Check the list of options given in the data attachment.

Show answer

Correct answer: 1, 13, 19, 23

Question 19 on its own page

Question 20

+3 marksOne correct option

The marks of students in a class is normally distributed with mean μ and standard deviation 10. If 10% of the students have scored more than 80, find the value of μ.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 20 on its own page

Question 21

+4 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 21 on its own page

Question 22

+2 marksNumerical answer

Two unbiased dice are thrown repeatedly. Find the expected number of trials needed to get the same value on both the dice.

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Correct answer: 6

Question 22 on its own page

Question 23

+4 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • D
Question 23 on its own page