---
id: 20260114133159
title: Expected Value
type: permanent
created: 2026-01-14T18:31:59Z
modified: 2026-01-14T18:41:57Z
tags: []
---

# Expected Value
Expected value is pretty much the mean of a function, but
more specifically, it's the weighted average of all possible
outcomes of a function:

$$ \hat X = E{X} $$

If we have an estimate of a posterior using [[Bayes'
Theorem]], we can get the following result:

$$ \hat X = \sum_i X^i \hat{Pr}(X^i|Y) $$