pairwise independent events

两两独立事件

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

Other names / variants: pairwise independence

Translation evidence: Literature usage

Meaning in context

A family of events in one probability space for which $P(A_i\cap A_j)=P(A_i)P(A_j)$ whenever $i\ne j$.

同一概率空间中的事件族，任意两个不同事件的交概率都等于各自概率之积。

Example

For two independent fair bits, events 'first is 1', 'second is 1', and 'bits differ' are pairwise independent but their triple intersection is empty.

Usage and distinctions

Checking all pairs does not establish mutual independence for three or more events.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Richard Weber — Probability§5.3 Independence of multiple events, pairwise-independence discussion · Checked 2026-10-14

Translation sources

1. 李东风 — 应用随机过程（北京大学）§1.5.1 独立性，注2：两两独立不一定相互独立 · Checked 2026-10-14

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