probability mass function

概率质量函数

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

Other names / variants: PMF · pmf

Translation evidence: Literature usage

Meaning in context

For a discrete random variable with countable support SS, the function p(x)=P(X=x)p(x)=P(X=x) on SS, whose nonnegative values sum to one.

离散随机变量在各个可能取值处的概率函数，所有非负质量之和为1。

Example

A fair binary variable has p(0)=p(1)=1/2p(0)=p(1)=1/2.

Usage and distinctions

Mass is point probability; density with respect to length is not point probability.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Richard Weber — Probability§7.2 Discrete random variables, probability mass function · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程（北京大学）§1.2.3 常用分布，离散型随机变量与PMF · Checked 2026-10-14
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