GATE Questions & Answers of Probability and Statistics Electronics and Communication Engg

The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is _______ 

Two random variables X and Y are distributed according to

fX,Yx,y=x+y,   0x1, 0y10,         otherwise

The probability PX+Y1 is ________

The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed  repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is __________

Suppose $ A $ and $ B $ are two independent events with probabilities $ P(A)\neq0 $ and $ P(B)\neq0 $. Let A and B be their complements Which of the following statement is FALSE?

In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _____

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ______

Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability 15 of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office 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 fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is