Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
| (i) | \begin{equation} \mathbb{E} |X| < \infty \end{equation} |
| (ii) | $f$ is a D209: Probability density function for $X$ |
Then
\begin{equation}
\mathbb{E}(X)
= \int^{\infty}_{-\infty} x f(x) \, d x
\end{equation}