Question: Let (X) be a random variable that has moment generating function (m(t)) that converges on some radius (|t| leq b) for some (b>0). Using induction,

Let $X$ be a random variable that has moment generating function $m(t)$ that converges on some radius $|t| \leq b$ for some $b>0$. Using induction, prove that

\[\mu_{k}^{\prime}=\left.\frac{d^{k} m(t)}{d t^{k}}ight|_{t=0}\]

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