expected value

The expected value of a random variable is the average value it will take when weighted by the probability of each outcome, aka the mean. It is a measure of center.

Formally,
the expected value of a discrete random variable $X$ with probability mass function $p (x)$ is given by

E [X] = \sum x \cdot p (x)

and the expected value of a continuous random variable $X$ with probability density function $f (x)$ is given by

E [X] = \int_{- \infty}^{\infty} x \cdot f (x) d x

In general,
the expected value of a function $h (X, Y)$ of two random variables is given by

E [h (X, Y)] = \sum_{x} \sum_{y} h (x, y) \cdot p (x, y)

in the discrete case, or

E [h (X, Y)] = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} h (x, y) \cdot f (x, y) d x d y

in the continuous case.

This can be trivially generalized to any function of any finite number of random variables.