binomial distribution

二项分布

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

Translation evidence: Literature usage

Meaning in context

For an integer $n\ge0$ and $0\le p\le1$, the law of the sum of $n$ independent Bernoulli$(p)$ variables; its mass is $\binom nk p^k(1-p)^{n-k}$ for $0\le k\le n$.

n个独立、成功概率均为p的0/1变量之和的分布，n为非负整数；端点参数按退化分布理解。

Example

For $n=3,p=1/2$, the probability of two successes is $3/8$.

Usage and distinctions

Independent trials with different success probabilities do not generally give a binomial law.

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）§1.2.3.3 二项分布 · Checked 2026-10-14

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