Raw Moment of Poisson Distribution

Theorem
Let $X$ be a discrete random variable with the Poisson distribution with parameter $\lambda$.

Let $n$ be a strictly positive integer.

Then the $n$th raw moment $\expect {X^n}$ of $X$ is given by:


 * $\displaystyle \expect {X^n} = \sum_{k \mathop = 0}^n \lambda^k {n \brace k}$

where $\displaystyle {n \brace k}$ is a Stirling number of the second kind.