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)={{:(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 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)={{:(ke^(-x/3), "for " x gt 0), (0, "for " x le 0):} Find the distribution function

The probability density function of X is given by f(x) = {(ke^(-x/3),"for" " "xgt0),(0, "for" " " xlt=0):} Find (i) the value of k (ii) the distribution function (iii) P(X lt 3) (iv) P(5lt=X) (v) P(X lt=4) .