statistics

Poisson pmf

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The_Don. answered · 01/07/2021

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Poisson PMF

A discrete random Variable $x$ is said to have a Poisson Distribution, with parameter $λ > 0$ if it has a PMF (Probability Mass Function) given by;

$P r (X = k) = \frac{λ^{k} e^{- λ}}{k!}$

where

$e$ is the Euler's number

k is the number of occurrences

$λ$ is the expected value of X and also the variance (It is a positive real number)

Thus the Poisson PMF is given by;

$P r (X = k) = \frac{λ^{k} e^{- λ}}{k!}$

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