Definition – Covariance. – Math-reference.net

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1. Definition

Definition

Let $X$ and $Y$ be random variables for a probability space. The covariance of $X$ and $Y$ is defined as

$cov(X,Y) = E[(X-\bar X)(Y-\bar Y)]$

We define the variance of a single random variable $X$ as

$var(X) = cov(X,X) = E[(X-\bar X)^2]$