Expected value

The expected value is the mean you would see over many repetitions of the random process, and it need not be a value the variable can actually take. For example, a game that pays 2 dollars with probability 0.5 and nothing with probability 0.5 has expected value $2(0.5) + 0(0.5) = 1$ dollar. In general it is written $E(X) = \mu_X = \sum x_i \, p_i$ (E of X, the mean of X, sums each value times its probability). It is the balance point of the probability distribution.