# ~ 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:

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

1

Wikipedia contributors. (2021, March 17). Expected value. Wikipedia. https://en.wikipedia.org/wiki/Expected_value