\begin{definition}[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:
:$\mu'_n = \expect {X^n}$
where $\expect {\, \cdot \,}$ denotes the expectation function.
That is:
:$\mu'_n = \ds \sum_{x \mathop \in \Omega_X} x^n \map {p_X} x$
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'''.
\end{definition}