The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.
Overview
The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value. For a discrete random variable, $X$, the expected value is
$$ E(X) = \sum_{x} x P(X=x) $$
for a continuous variable with probability density function $p(x)$,
$$ E(X) = \int_{-\infty}^{\infty} x p(x) dx $$
