ThmDex – An index of mathematical definitions, results, and conjectures.
F12721
Formulation 2
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}