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

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 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(X lt 3)

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 distribution function

The probability density function of the random variable X is given by f(x)={{:(16xe^(-4x), "for " x gt 0), (0, "for " x le 0):} find the mean and variance of X