GATE DA concept:random-variables PYQs & Answers — Page 2

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concept:random-variables

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

Topic practice 20 questionsPage 2 of 2

Let

, where

is a normal random variable with mean

and variance

. The variance of

Your answerChoose one option.

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Consider the cumulative distribution function (CDF) of a random variable

The value of

Your answerChoose one option.

0.625

0.25

0.5

0.5625

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A random variable

is said to be distributed as

, denoted by

, if

for

. Let

, where

be independent and identically distributed random variables with

. The value of

, after approximation through Central Limit Theorem, is given by (Recall that

)

Your answerChoose one option.

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For

, the floor function is denoted by

and defined as follows

where

is an integer. Let

, where

is an exponentially distributed random variable with mean

, where

denotes natural logarithm. For any positive integer

, one can write the probability of the event

as follows

The value of

Your answerChoose one option.

0.1

0.01

0.5

0.434

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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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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 a joint probability density function of two random variables X and Y

Then,

is _____.

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Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables:

Diagram for Data Science and Artificial Intelligence question 64

The value of

______ (rounded off to three decimal places).

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Two fair coins are tossed independently. X is a random variable that takes a value of 1 if both tosses are heads and 0 otherwise. Y is a random variable that takes a value of 1 if at least one of the tosses is heads and 0 otherwise.

The value of the covariance of X and Y is ______ (rounded off to three decimal places).

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GATE DA concept:random-variables PYQs

Question 36

Question 39

Question 40

Question 41

Question 11

Question 56

Question 57

Question 59

Question 64

Question 65