~ Expected value

The expected value of a variable $X$ is a generalization of the mean of said value.¹ In other words, it is the weighted mean.

In the discrete case, consider a set of data $X = {x_1, …, x_N}$ where $p_i$ represents the probability of $x_i$ occuring. Here the expected value is:

$$ \mathbb{E}[X] = \sum_{i = 1}^N p_i x_i $$