Find the mean of a random variable X, whose probability density function is `f(x)={{:(lambdae^(-lambdax), "for " x ge 0), (0, "otherwise"):}`.

Find the mean and variance of a random variable X , whose probability function is f(x) = {(lambdae^(-lambdax),"for"" "xgt=0),(0,"otherwise"):}

A discrete random variable X has probability mass function P(x) then

If X is the random variable with probability density function f(x) is given by f(x)={{:(x+1, -1 le x lt 0), (-x+1, 0 le x lt 1), (0,"otherwise"):} then find (i) the distribution function F(x) (ii) P(-0.5 le X le 0.5)

A random variable X has the following probability mass function Find k

The probability density function of X is given by f(x)={{:(ke^(-x/3), "for " x gt 0), (0, "for " x le 0):} Find P(X le 4)

The probability density function of X is given by f(x)={{:(ke^(-x/3), "for " x gt 0), (0, "for " x le 0):} Find P(5 le X)

The probability density function of X is given by f(x)={{:(ke^(-x/3), "for " x gt 0), (0, "for " x le 0):} Find P(X lt 3)

The probability density function of X is given by f(x)={{:(kxe^(-2x), "for " x gt 0), (0, "for " x le 0):} Find the value of k.

The probability density function of X is given by f(x)={{:(ke^(-x/3), "for " x gt 0), (0, "for " x le 0):} Find the value of k