ThmDex – An index of mathematical definitions, results, and conjectures.
F12670
Formulation 1
Let $X, Y \in \text{Random}(\Omega \to \mathbb{R})$ each be a D3161: Random real number such that
(i) \begin{equation} \mathbb{E} |X|, \mathbb{E} |Y| < \infty \end{equation}
Let $\alpha, \beta \in \mathbb{C}$ each be a D1207: Complex number.
Then \begin{equation} \mathbb{E}(\alpha X + \beta Y) = \alpha \mathbb{E} X + \beta \mathbb{E} Y \end{equation}