\begin{definition}[Definition:Central Moment]
Let $X$ be a random variable on some probability space with mean $\mu$. 
Then the '''$n$th central moment of $X$''', usually denoted $\mu_n$, is defined as: 
:$\mu_n = \expect {\paren {X - \mu}^n}$
where $\expect X$ denotes the expectation of $X$.
That is, the $n$th central moment of $X$ is its $n$th moment about $\mu$. 
The second central moment of $X$ is the variance of $X$, and is instead usually denoted $\sigma^2$.
\end{definition}