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

#### Probability and Statistics 11 Question(s)

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

The probability $P\left(X+Y\le 1\right)$ 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 $\overline{)A}$ and $\overline{)B}$ 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 $\frac{1}{5}$ 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