Poisson distribution

泊松分布

Probability · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: Poisson分布

Translation evidence: Literature usage

Meaning in context

For λ>0\lambda>0, a law on nonnegative integers with P(X=k)=e−λλk/k!P(X=k)=e^{-\lambda}\lambda^k/k!.

在非负整数上取值、k处概率为指数因子与λ的k次方除以k阶乘的分布，参数λ为正。

Example

For λ=2\lambda=2, P(X=0)=e−2P(X=0)=e^{-2} and E[X]=2E[X]=2.

Usage and distinctions

The parameter is the mean count, not the probability of a single event; both mean and variance equal lambda.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on Probability§8.1.2 Poisson distribution · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程（北京大学）§1.2.3.4 泊松分布 · Checked 2026-10-14
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