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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 > 0的'''<font color="#ff8000">泊松分布</font>'''，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 > 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>

The positive real number λ is equal to the expected value of X and also to its variance<ref>For the proof, see :

The positive real number λ is equal to the expected value of X and also to its variance<ref>For the proof, see :

正实数等于 x 的期望值和方差 < ref > 相关证明，请参阅:

正实数'''λ'''等于 x 的期望值和方差 < ref > 相关证明，请参阅:

[http://www.proofwiki.org/wiki/Expectation_of_Poisson_Distribution Proof wiki: expectation] and [http://www.proofwiki.org/wiki/Variance_of_Poisson_Distribution Proof wiki: variance]</ref>

[http://www.proofwiki.org/wiki/Expectation_of_Poisson_Distribution Proof wiki: expectation] and [http://www.proofwiki.org/wiki/Variance_of_Poisson_Distribution Proof wiki: variance]</ref>