independent events

独立事件

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

Other names / variants: independence of events · 事件独立性

Translation evidence: Literature usage

Meaning in context

Events AiA_i are mutually independent if every finite subfamily satisfies P(⋂i∈JAi)=∏i∈JP(Ai)P(\bigcap_{i\in J}A_i)=\prod_{i\in J}P(A_i).

任意有限子族的交事件概率都等于各事件概率之积时，该事件族相互独立。

Example

Heads on the first and second toss of independent fair coins are independent events.

Usage and distinctions

Pairwise independence checks pairs only and need not imply mutual independence.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Richard Weber — Probability§§5.2–5.3 Independence of two / multiple events · 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，定义1.15及注2 · Checked 2026-10-14
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