Expected value

The expected value of a random variable $X$ taking integer values between 1 and $n$ is defined to be $\mathrm{E}(X) = \sum_{k=1}^{n}{k \times \mathrm{Pr}(X = k)}$.

We also may talk of the "expected number" of given events occurring. If $A_1, A_2, \ldots, A_m$ form a collection of events, then the expected number of these events that will occur is the sum of their probabilities: $\mathrm{Pr}(A_1) + \mathrm{Pr}(A_2) + \cdots + \mathrm{Pr}(A_m)$. See indicator random variable for a precise discussion of this formula.