The Darth Vader rule

Abstract

\emph{Using Henstock's generalized Riemann integral, we show that, for any almost surely non-negative random variable $X$ with probability density function $f_{X}$ and survival function $s_{X}(x):=\int_{x}^{\infty }f_{X}(t)dt$, the expected value of $X$ is given by $\mathbf{E}% (X)=\int_{0}^{\infty }s_{X}(x)dx$.}