Moment in terms of Moment Generating Function

Theorem
Let $X$ be a random variable.

Let $M_X$ be the moment generating function of $X$.

Then:


 * $\mathbb E \left[{X^n}\right] = M^{\left({n}\right)}_X \left({0}\right)$

where:
 * $n$ is a non-negative integer
 * $M^{\left({n}\right)}_X$ denotes the $n$th derivative of $M_X$.

Proof
Setting $t = 0$ yields the result.