Central Moments of a Random Variable

The n-th central moment of $X$ is defined as

$$\mathbb{E}\{(X-{\mu }_X{)}^n\}={\int }_{\mathbb{R}}(x-{\mu }_X{)}^n{f}_X(x)dx$$

Special cases of the central moment

• $n=1$: Equals to zero
• $n=2$: Provides the Variance ${\sigma }_X^2$