Danes-Vault/Zettelkasten/Permanent Notes/20260114133159-expected-value.md

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

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)