For any Random variable $X$ and $n=1,2,3,…$, we have the following definitions.

- The $n$th
**moment**of $X$ is $E(X_{n})$. When $n=1$, this is just the Expectation. - The $n$th
**central moment**of $X$ is $E([X−μ]_{n})$, where $μ=E(X)$. When $n=2$, this is just the Variance. - The $n$th
**standardized moment**of $X$ is $E([σX−μ ]_{n})$.

Moments are often used to summarize properties about a distribution. If expectations are undefined, then so are the moments.

- The expectation and variance are the 1st moment and 2nd central moments, respectively.
- Skewness is the 3rd standardized moment, and excess kurtosis is the 4th standardized moment, minus 3.

Related to moments are Moment generating functions.