Result
R3956: Expectation of random unsigned basic number by integrating tail probabilities shows that
\begin{equation}
\mathbb{E} X
= \int^{\infty}_0 \mathbb{P}(X > t) \, d t
\end{equation}
By definition, $F(t) : = \mathbb{P}(X \leq t)$. Applying result
R3558: Probability of level sets for random basic number, we may thus conclude that
\begin{equation}
\mathbb{E} X
= \int^{\infty}_0 \mathbb{P}(X > t) \, d t
= \int^{\infty}_0 (1 - \mathbb{P}(X \leq t)) \, d t
= \int^{\infty}_0 (1 - F(t)) \, d t
\end{equation}
