Definition:Moment (Probability Theory)/Discrete

Definition
Let $X$ be a discrete random variable.

Then the $n$th moment of $X$ is denoted $\mu'_n$ and defined as:
 * $\mu'_n = E \left({X^n}\right)$

where $E$ denotes the expectation function.

That is:
 * $\displaystyle \mu'_n = \sum_{x \mathop \in \Omega_X} x^n p_X \left({x}\right)$

whenever this sum converges absolutely.

It can be seen from its definition that the expectation of a discrete random variable is its first moment.

Also see the relation between the variance of a discrete random variable and its second moment.