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 $\mathbf{E}%
(X)=\int_{0}^{\infty }s_{X}(x)dx$.}