Expectation of Variable

The expectation of a random variable $X$ is the weighted average of the possible values of $X$

$$E[X]=\sum _{k}k\cdot \text{Prob}(X=k)$$

Given $X$ and $Y$ are any two random variables and $a,b\in \mathbb{R}$, it follows:

$$\begin{array}{rl}E[aX+b]& =aE[X]+b\\ E[X+Y]& =E[X]+E[Y]\end{array}$$