Definition 73.
Let \(X\) be a discrete random variable taking values \(x_1, x_2, \dotsc, x_n\) with probabilities \(p_1, p_2, \dotsc, p_n\text{.}\) The expected value of \(X\) is:
\begin{gather*}
\E(X) = \sum_{i=1}^n x_ip_i = x_1p_1 + x_2p_2 + \dotsb + x_np_n.
\end{gather*}