Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) | $Z, W : \Omega \to \mathbb{C}$ are each a D4877: Random complex number on $P$ |
(ii) | \begin{equation} \mathbb{E} |Z|, \mathbb{E} |W| < \infty \end{equation} |
(iii) | $\alpha, \beta \in \mathbb{R}$ are each a D993: Real number |
Then
\begin{equation}
\mathbb{E}(\alpha Z + \beta W)
= \alpha \mathbb{E} Z + \beta \mathbb{E} W
\end{equation}