> [!NOTE] Theorem > Let $X$ be a [[Random Variables|real-valued random variable]]. Let $M_{X}$ be the [[Moment generating function of real-valued random variable|moment generating function]] of $X.$ If $M_{X}$ is defined on $(-a,a)$ for some $a>0,$ then $X$ has all [[Raw Moment of Real-Valued Random Variable|raw moments]] and they're given by $\mathbb{E}[X^{k}]=M_{X}^{(k)}(0)$where $M^{(k)}_{X}$ denotes the $k$-th derivative of $M_{X}.$ **Proof**: