random variable

随机变量

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

Other names / variants: r.v.

Translation evidence: Literature usage

Meaning in context

A real-valued measurable map X:(Ω,F)→(R,B(R))X:(\Omega,\mathcal F)\to(\mathbb R,\mathcal B(\mathbb R)) on a probability space.

概率空间上取实数值的可测函数；每个Borel集合的原像必须是事件。

Example

If AA is an event, X=1AX=1_A is a random variable.

Usage and distinctions

A random variable is a function; its observed value and its distribution are different objects.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on ProbabilitySection 2, Random variables, opening definition and indicator example · 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，定义1.6 · Checked 2026-10-14
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