exponential distribution

指数分布

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

Translation evidence: Literature usage

Meaning in context

For rate λ>0\lambda>0, the nonnegative law with survival probability P(X>t)=e−λtP(X>t)=e^{-\lambda t} for t≥0t\ge0.

速率参数λ为正的非负连续分布，超过非负t的概率为exp(−λt)。

Example

With rate 22, P(X>1)=e−2P(X>1)=e^{-2} and E[X]=1/2E[X]=1/2.

Usage and distinctions

Rate lambda is the reciprocal of the mean; some texts parameterize by the mean instead.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on Probability§8.2.2 Exponential distribution · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程（北京大学）§1.2.3.13 指数分布 · Checked 2026-10-14
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