GATE Questions & Answers of Probability and Statistics Electrical Engineering

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n-3) is

Consider a dice with the property that the probability of a face with n dots showing up is proportional to n. The probability of the face with three dots showing up is ________.

Let X be a random variable with probability density function

fx=0.2,for x10.1,for 1<x40,otherwise

 

The probability P(0.5 < X < 5) is ___________.

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 ________.

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

Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The probability that max[X, Y] is less than 1/2 is

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is

Assume for simplicity that N people, all born in April (a month of 30 days), are collected in a room. Consider the event of at least two people in the room being born on the same date of the month, even if in different years, e.g. 1980 and 1985. What is the smallest N so that the probability of this event exceeds 0.5?

X  is a uniformly distributed random variable that takes values between 0 and 1.The value of E{X3} will be

A loaded dice has following probability distribution of occurrences

Dice value 1 2 3 4 5 6
Probability 1/4 1/8 1/8 1/8 1/8 1/4

If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is