"If X is non-negative, then E(X) = Integral(0 to infinity) of (1-F(x))dx, where F(x) is the cumulative distribution function of X." ============================ First of all, does X have to be a continuous random variable here? Or will the above result hold for both continuous and discrete random variable X? Secondly, the source that states this result gives no proof of it. I searched the internet but was unable to find a proof of it. I know that by definition, since X is non-negative, we have E(X) = Integral(0 to infinity) of x f(x)dx where f(x) is the density function of X. What's next? Thanks for any help!