Normalizing constant: Difference between revisions

Revision as of 20:16, 10 December 2020

Revision as of 20:18, 10 December 2020

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Similarly,

:<math>\sum_{n=0}^\infty \frac{\lambda^n}{n!}=e^{-\lambda} ,</math>

and consequently

:<math>f(n)=\frac{\lambda^n e^{-\lambda}}{n!} </math>

is a probability mass function on the set of all nonnegative integers.<ref>Feller, 1968, p. 156.</ref> This is the probability mass function of the [[Poisson distribution]] with expected value &lambda;.