covariance

协方差

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Translation evidence: Literature usage

Meaning in context

For square-integrable real X,YX,Y, Cov⁡(X,Y)=E[(X−E[X])(Y−E[Y])]\operatorname{Cov}(X,Y)=E[(X-E[X])(Y-E[Y])].

两个二阶矩有限变量的中心化乘积的期望。

Example

If Y=2XY=2X and Var⁡(X)=3\operatorname{Var}(X)=3, then Cov⁡(X,Y)=6\operatorname{Cov}(X,Y)=6.

Usage and distinctions

Zero covariance need not imply independence: symmetric XX and X2X^2 can be dependent and uncorrelated.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Richard Weber — ProbabilityChapter 10, Covariance and correlation, covariance 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，协方差 · Checked 2026-10-14
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