Let $X, Y \in \text{Random}(\Omega \to \mathbb{R})$ each be a D3161: Random real number such that
Let $\alpha, \beta \in \mathbb{C}$ each be a D1207: Complex number.
(i) | \begin{equation} \mathbb{E} |X|, \mathbb{E} |Y| < \infty \end{equation} |
Then
\begin{equation}
\mathbb{E}(\alpha X + \beta Y)
= \alpha \mathbb{E} X + \beta \mathbb{E} Y
\end{equation}