Definition:Moment (Probability Theory)/Discrete

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

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.