Factorial moment generating function: Difference between revisions

Revision as of 14:56, 14 March 2006

Revision as of 15:01, 14 March 2006

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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_{0}^\infty \frac{\lambda^x e^{-\lambda}}{x!} \,\mathrm{d}x</math>

:::<math> = e^{-\lambda(1-t)}</math>

and thus we have

:<math>E( (X)_n )=\lambda^n.</math>