Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) | \begin{equation} \mathbb{E} |X|^2 < \infty \end{equation} |
Then
\begin{equation}
\mathbb{E} X
= \underset{\lambda \in \mathbb{R}}{\text{arg min}} \; \mathbb{E} |X - \lambda|^2
\end{equation}