GATE DA concept:random-variables PYQs & Answers

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concept:random-variables

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Questions 1–10 of 20. Imported answers require independent review unless marked reviewed.

Topic practice 20 questionsPage 1 of 2

Suppose a random variable

follows Normal

distribution with probability density function

and cumulative distribution function

. Another random variable

follows

distribution with probability density function

and cumulative distribution function

. Let

be the positive real number for which

Which of the following statements is/are correct?

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

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Let

be an exponentially distributed random variable with mean

. If

, then the conditional probability

is ________ . (Rounded off to two decimal places)

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Let

and

be two independent random variables.

follows Bernoulli

distribution and

follows Normal

distribution.

Which of the following options is the variance of

Your answerChoose one option.

100

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Let

independent random variables. Each of the random variables follows

distribution. Define

. Which of the following statements is/are correct?

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

follows Chi-square distribution with

degrees of freedom.

follows Chi-square distribution with

degrees of freedom.

follows exponential distribution with mean 2.

follows Chi-square distribution with 2 degrees of freedom.

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Let

be a discrete valued random variable with cumulative distribution function

. Which of the following statements is/are correct?

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

is always a positive function.

is a non-decreasing function.

has jump discontinuity.

is a left continuous function.

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Let

be a random variable that follows

distribution. The conditional distribution of the random variable

given

is the

distribution.

The value of

is ________ . (Answer in integer)

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Suppose

and

are random variables. The conditional expectation of

given

is denoted by

. Then

equals

Your answerChoose one option.

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Let

be a continuous random variable whose cumulative distribution function (CDF)

, for some

, is given as follows:

If the median of

is 3, then what is the value of

Your answerChoose one option.

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Let

, where

is a standard normal random variable, and

are two unknown constants. It is given that

where

denotes the expectation of random variable

. The values of

are:

Your answerChoose one option.

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It is given that

for an exponentially distributed random variable

with

, where

denotes the expectation of

. What is the value of

(ln denotes natural logarithm)

Your answerChoose one option.

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GATE DA concept:random-variables PYQs

How to practice concept:random-variables

Question 28

Question 34

Question 44

Question 53

Question 54

Question 63

Question 11

Question 19

Question 20

Question 21