Category:Definitions/Central Moments

This category contains definitions related to Central Moments.
Related results can be found in Category:Central Moments.

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 $\sigma^2$.