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Suppose ''X'' has a [[Poisson distribution]] with [[expected value]] λ, then the factorial moment generating function of ''X'' is
:<math>M_X(t) = \sum_{x=0}^\infty \frac{\lambda^x e^{-\lambda}}{x!} \,</math>
:::<math> = e^{-\lambda(1-t)}</math>
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