Definition:Central Moment

Definition
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 $\sigma^2$.

Also known as
Some sources refer to the $n$th central moment of a random variable as its $n$th moment about the mean.

Also see

 * Definition:Moment (Probability Theory)
 * Definition:Raw Moment
 * Definition:Standardized Moment