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A discrete random variable X is said to have a Poisson distribution with parameter λ > 0, if, for k = 0, 1, 2, ..., the probability mass function of X is given by:

A discrete random variable X is said to have a Poisson distribution with parameter λ > 0, if, for k = 0, 1, 2, ..., the probability mass function of X is given by:

一个离散的随机变量 x 被称为具有参数λ> 0的泊松分布，如果对于 k = 0,1,2，... ，x 的概率分布函数是:

一个离散的随机变量 x 被称为具有参数λ > 0的泊松分布，如果对于 k = 0,1,2，... ，x 的概率分布函数是:

:<math>\!f(k; \lambda)= \Pr(X = k)= \frac{\lambda^k e^{-\lambda}}{k!},</math>

:<math>\!f(k; \lambda)= \Pr(X = k)= \frac{\lambda^k e^{-\lambda}}{k!},</math>

<math>\!f(k; \lambda)= \Pr(X = k)= \frac{\lambda^k e^{-\lambda}}{k!},</math>

<math>\!f(k; \lambda)= \Pr(X = k)= \frac{\lambda^k e^{-\lambda}}{k!},</math>

< math > ! f (k; lambda) = Pr (x = k) = frac { lambda ^ k e ^ {-lambda }}{ k！} ，</math >  

< math > \!f(k; \lambda) = \Pr (x = k) = \frac { \lambda ^ k e ^ {-\lambda }}{ k！},</math >  

where

where