variance

方差

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

Translation evidence: Literature usage

Meaning in context

For $E[X^2]<\infty$, the variance is $\operatorname{Var}(X)=E[(X-E[X])^2]$.

二阶矩有限的随机变量与其均值之差的平方的期望。

Example

A fair $0/1$ variable has variance $1/4$.

Usage and distinctions

Variance has squared units; standard deviation is its nonnegative square root.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gregory F. Lawler — Notes on ProbabilitySection 2, variance definition · Checked 2026-10-14

Translation sources

1. 李东风 — 应用随机过程（北京大学）§1.3.2 数字特征，定义1.11，方差 · Checked 2026-10-14

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