Expected value

For a discrete random variable x with sample space \(S_X\) and PMF \(p(x)\). The expected value is

\[ E(X)=\mu X=\sum_{x\in S_X}xp(x) \]

Example: Let X be the random variable with PMF

x -1 1 2
p(x) 1/3 1/6 1/2