Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
Let $n \in \mathbb{N}$ be a D996: Natural number such that
| (i) | $f$ is a D209: Probability density function for $X$ |
| (i) | \begin{equation} \mathbb{E} |X|^n < \infty \end{equation} |
Then
\begin{equation}
\mathbb{E}(X^n)
= \int^{\infty}_{-\infty} x^n f(x) \, d x
\end{equation}