Let X 0 be a non-negative random variable, with a given (cumulative) distribution F. Show that E{X} = 0 P{X > x}dx, and also show that in general, for any p 1 E{Xp } = 0 pxp1P{X > x}dx. You can assume (although not necessary) that the probability density function (pdf) fX(x) = dF(x)/dx exists at all x 0. Hint: Assuming pdf function, try integration by part, noting that P{X > x} = 1 x 0 fX(u)du