ThmDex – An index of mathematical definitions, results, and conjectures.
F8997
Formulation 0
Let $X \in \text{Random} [0, \infty]$ be a D5101: Random unsigned basic number such that
(i) $F : \mathbb{R} \to [0, 1]$ is a D205: Probability distribution function for $X$
Then \begin{equation} \mathbb{E} (X) = \int^{\infty}_0 (1 - F (t)) \, d t \end{equation}