GATE ME concept:random-variables PYQs & Answers

Questions 1–7 of 7. Imported answers require independent review unless marked reviewed.

Let

be a continuous random variable defined on

such that its probability density function

for

and 0 otherwise. Let

. Then the expected value of

is _____. (rounded off to 2 decimal places)

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Let a random variable

follow Poisson distribution such that

The value of

is __________ (round off to 2 decimal places).

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Consider a binomial random variable

. If

are independent and identically distributed samples from the distribution of

with sum

, then the distribution of

can be approximated as

Your answerChoose one option.

Exponential

Bernoulli

Binomial

Normal

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The sum of two normally distributed random variables X and Y is

Your answerChoose one option.

always normally distributed

normally distributed, only if X and Y are independent

normally distributed, only if X and Y have the same standard deviation

normally distributed, only if X and Y have the same mean

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Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is ______ (round off to 2 decimal places).

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Let

be two independent normal random variables with means

and standard deviations

, respectively. Consider

;

. Then,

Your answerChoose one option.

Y is normally distributed with mean 0 and variance 1

Y is normally distributed with mean 0 and variance 5

Y has mean 0 and variance 5, but is NOT normally distributed

Y has mean 0 and variance 1, but is NOT normally distributed

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Let

and

be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then

Your answerChoose one option.

exponentially distributed with mean 1/6

exponentially distributed with mean 2

normally distributed with mean 3/4

normally distributed with mean 1/6

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GATE ME concept:random-variables PYQs

How to practice concept:random-variables

Question 44

Question 47

Question 5

Question 1

Question 35

Question 26

Question 27