GATE ECE Probability and Statistics PYQs & Answers

Questions 1–10 of 17. Imported answers require independent review unless marked reviewed.

Let X, N, Y and Z be random variables. The variables X and N are independent of each other. X is uniformly distributed between -1 and 1; N follows Normal distribution with zero mean and unity variance. Y and Z are defined as,

and

. Which of the following pairs represents the values of correlation between X and Y and that between X and Z?

Your answerChoose one option.

1/3 and 0

1/3 and 1/9

1/3 and 1/3

1 and 0

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.

What is the probability that the two balls drawn have different colours?

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable

denote the sum of the outcomes obtained.

The expectation of

is ______ (rounded off to two decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that X ≥ Y is ______ .

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A random variable

, distributed normally as

, undergoes the transformation

, given in the figure. The form of the probability density function of

(In the options given below,

are non-zero constants and

is piece-wise continuous function)

Diagram for Electronics and Communication Engineering question 36

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Two continuous random variables

and

are related as

Let

and

denote the variances of

and

, respectively. The variances are related as

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A box contains the following three coins. I. A fair coin with head on one face and tail on the other face. II. A coin with heads on both the faces. III. A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is ______ bits.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A binary random variable

takes the value +2 or −2. The probability

. The value of

(rounded off to one decimal place), for which the entropy of

is maximum, is ______.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let

and

denote the labels corresponding to the outcomes of those tosses. For a random variable

, defined as

, the expected value

(rounded off to two decimal places) is ______.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE ECE Probability and Statistics PYQs

How to practice Probability and Statistics

Question 38

Question 13

Question 58

Question 33

Question 36

Question 3

Question 27

Question 51

Question 22

Question 25