[[Real random variable]]
# Symmetric distribution

A [[real random variable]] $X : \xi \to \mathbb{R}$ is said to have a **symmetric distribution** about $\mu$ iff $X-\mu$ has the same distribution as $\mu - X$. #m/def/prob 
It follows that $\mu$ is the [[Expectation]] if $\Ex[X]$ exists.

## Properties

- Every odd [[Statistical moment|central moment]] and [[Statistical moment|standardized moment]] of a symmetrically distributed random variable is zero, e.g. the [[Skewness]].


#
---
#state/tidy | #lang/en | #SemBr