Engineering Mat...

A random variable X had Poisson distribution. If 2P(X = 2) = P(X = 1) + 2P (X = 0) then the variance of X is

What is the variance of the random variable X whose probability mass function is given below?

X is uniformly distributed in (-2, 3). Which of the following is/are correct?

Out of 800 families with 4 children each, how many families would be expected to have 2 boys and 2 girls.

Consider a sequence of independent Bernoulli trials with probability of success in each trial being \(\frac{1}{5}\). Then which of the following statements is/are TRUE?

Let Harsh and Dinesh be the two players playing chess and their chances of winning a game are in the ration 4:3 respectively. What is the chance of Dinesh winning at least 4 game out of five games played?

Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

A random variable X has a probability density function \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{k\;{x^n}{e^{ - x}}\;;\;x \ge 0}\\{0\;;\;otherwise}\end{array}} \right.\) (n is an integer) with mean 3. The values of {k, n} are