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::<math>E\left((x)_n\right)=M_X^{(n)}(1)=\left.\frac{\mathrm{d}^n}{\mathrm{d}t^n}\right|_{t=1} M_X(t).</math>
==Example
Suppose ''X'' has a [[Poisson distribution]] with [[expected value]] λ, then the factorial moment generating function of ''X'' is
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