GATE DA Probability and Statistics PYQs & Answers — Page 2

Questions 11–20 of 23. Imported answers require independent review unless marked reviewed.

Consider a coin-toss experiment where the probability of head showing up is

. In the

coin toss, let

if head appears, and

if tail appears. Consider

where

is the total number of independent coin tosses. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

increases, variance of

decreases

Variance of

does not depend on

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A bag contains 5 white balls and 10 black balls. In a random experiment,

balls are drawn from the bag one at a time with replacement. Let

denote the total number of black balls drawn in the experiment.

The expectation of

denoted by

______ (Round off to one decimal place)

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Consider the following statements: (i) The mean and variance of a Poisson random variable are equal. (ii) For a standard normal random variable, the mean is zero and the variance is one.

Which ONE of the following options is correct?

Your answerChoose one option.

Both (i) and (ii) are true

(i) is true and (ii) is false

(ii) is true and (i) is false

Both (i) and (ii) are false

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Three fair coins are tossed independently. T is the event that two or more tosses result in heads. S is the event that two or more tosses result in tails.

What is the probability of the event

Your answerChoose one option.

0.5

0.25

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Let the minimum, maximum, mean and standard deviation values for the attribute income of data scientists be ₹4600, ₹17000, ₹9600, and ₹2100, respectively. The z-score normalized income value of ₹10600 is closest to which ONE of the following options?

Your answerChoose one option.

0.217

0.476

0.623

2.304

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The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is _____.

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A fair six-sided die (with faces numbered 1, 2, 3, 4, 5, 6) is repeatedly thrown independently.

What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen?

Your answerChoose one option.

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Let

be a random variable uniformly distributed in the interval

and

be a random variable uniformly distributed in the interval

. If

and

are independent of each other, the probability

is _____ (rounded off to three decimal places).

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Let

be a random variable exponentially distributed with parameter

. The probability density function of

is given by:

, where

and

indicate the expectation and variance of

, respectively, the value of

is _____ (rounded off to one decimal place).

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Consider two events T and S. Let

denote the complement of the event T. The probability associated with different events are given as follows:

Then,

is _____ (rounded off to two decimal places).

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GATE DA Probability and Statistics PYQs

Question 54

Question 61

Question 11

Question 12

Question 27

Question 34

Question 36

Question 56

Question 57

Question 58