GATE EE concept:random-variables PYQs & Answers

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concept:random-variables

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

Topic practice 7 questionsPage 1 of 1

Let X and Y be two real-valued random variables with E(X) = 1, E(Y) = 2, E(X²) = 4, E(Y²) = 9, and E(XY) = 0.9, where E denotes the expectation operator.

The value of α that minimizes E((X − αY)²) is __________ (Round off to one decimal place)

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Consider discrete random variables

and

with probabilities as follows:

Given

, the expected value of

Your answerChoose one option.

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Let

and

be continuous random variables with probability density functions

and

, respectively. Further, let

and

Which one of the following options is correct?

Your answerChoose one option.

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Let

be a discrete random variable that is uniformly distributed over the set

. Which of the following random variables is/are uniformly distributed?

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

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Let the probability density function of a random variable

be given as

The value of ‘a’ is ________.

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Let

be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of

for

. The mean of

is ____

Your answerChoose one option.

2.5

5.0

25.0

50.0

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A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable

denote the number of heads. The value of

, where

denotes the variance, equals

Your answerChoose one option.

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GATE EE concept:random-variables PYQs

How to practice concept:random-variables

Question 64

Question 15

Question 36

Question 29

Question 54

Question 8

Question 40