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:


 * $\expect {X^n} = \map { {M_X}^{\paren n} } 0$

where:
 * $n$ is a non-negative integer
 * ${M_X}^{\paren n}$ denotes the $n$th derivative of $M_X$
 * $\expect {X^n}$ denotes the expectation of $X^n$.

Proof
Setting $t = 0$ yields the result.