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GATE 2019: Engineering Mathematics Quiz 2

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Question 1

A continuous random variable X has a probability density function f(x) = e^–x, 0< x< ∞. Then P{X > 1} is

Question 2

Two fair dice are rolled and the sum r of the numbers turned up is considered

Question 3

Lifetime of an electric bulb is a random variable with density f(x) = kx² where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is ________.

Question 4

Two players A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is

Question 5

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colors that the candidate could bring. The probability that a candidate comes with all 3 pens having the same color is --------.

Question 6

A random variable X has probability density function f(x) as given below.

If the expected value E[X] = 2/3, then Pr[X < 0.5] is Signal flow graphs

Question 7

Consider a function z(x,y) be defined as

The value of

equals to

Question 8

A bag contains 40 balls numbered from 1, 2, 3, …., 40 out of which four are drawn and arranged in an ascending order (b₁ < b₂ < b₃ < b₄....). The probability that the third ball is numbered 25 is _________.

Question 9

The mean of two independent random variables X and Y are 1 and 1.5 respectively. The mean of the joint variable XY,

is _____.

Question 10

For a Poisson distribution having parameter

. The standard deviation of the distribution will be:

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ESE & GATE EE Engineering Mathematics

Nov 21ESE & GATE EE