Definition:Moment of Discrete Random Variable

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:

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

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.

Sources

• Geoffrey Grimmett: Probability: An Introduction (1986): $\S 4.3$