GATE DA topic:probality-statistics PYQs & Answers

Questions 1–10 of 13. Imported answers require independent review unless marked reviewed.

Let

be a randomly chosen non-empty subset of

Which of the following is the probability that the product of all the elements of

is even?

Your answerChoose one option.

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Suppose that a computer program provides a non-negative and integer-valued random solution to the equation

Which of the following is the probability that all of

in the provided solution are positive?

Your answerChoose one option.

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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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The number of bijections

from the set

to itself such that

, for all

, is ________ . (Answer in integer)

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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

Which of the following is the value of

Your answerChoose one option.

0.5

1.0

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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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A clinic specializes in testing for a disease D. The result of the test can be either positive or negative.

A study revealed that if a person suffers from the disease D, the test result in that clinic comes out positive 80% of the time, and negative 20% of the time. If a person is not suffering from the disease D, the test comes out positive 10% of the time and negative 90% of the time. It is also known that among the general population, the disease D occurs in 30% of the individuals.

If a person tests positive for D in that clinic, the probability that he/she actually suffers from the disease D is ________ . (Rounded off to two decimal places)

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GATE DA topic:probality-statistics PYQs

How to practice topic:probality-statistics

Question 19

Question 20

Question 28

Question 33

Question 34

Question 44

Question 45

Question 53

Question 54

Question 57