Bernoulli distribution

Bernoulli分布

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

Translation evidence: Literature usage

Meaning in context

A distribution supported on {0,1}\{0,1\} with P(X=1)=pP(X=1)=p and P(X=0)=1−pP(X=0)=1-p, where 0≤p≤10\le p\le1.

取值0和1的分布，其中1的概率为p，0的概率为1−p，且p介于0和1之间。

Example

An event indicator 1A1_A has Bernoulli distribution with parameter P(A)P(A).

Usage and distinctions

Bernoulli counts one success indicator; a binomial variable counts successes across a fixed number of independent trials.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on Probability§8.1.1 Bernoulli and Binomial · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程（北京大学）§1.2.3.2 Bernoulli分布 · Checked 2026-10-14
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