probability distribution

概率分布

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

Other names / variants: law · 分布

Translation evidence: Literature usage

Meaning in context

The probability measure induced by a random variable XX, given by μX(B)=P(X∈B)\mu_X(B)=P(X\in B) on Borel sets.

随机变量在取值空间上诱导的概率测度，即把每个Borel集合赋值为变量落入其中的概率。

Example

A fair binary indicator has mass 1/21/2 at each of 00 and 11.

Usage and distinctions

Identical distributions do not imply that two variables agree on their underlying probability space.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on ProbabilitySection 2, Random variables, distribution mu_X · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程（北京大学）§1.2.1 随机变量，分布与同一分布函数的说明 · Checked 2026-10-14
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