Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X, Y : \Omega \to \mathbb{R}$ are each a D3161: Random real number on $P$
(ii)	\begin{equation} \mathbb{E} |X|, \mathbb{E} |Y| < \infty \end{equation}
(iii)	$\alpha, \beta \in \mathbb{C}$ are each a D1207: Complex number

Then \begin{equation} \mathbb{E}(\alpha X + \beta Y) = \alpha \mathbb{E} X + \beta \mathbb{E} Y \end{equation}

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}