2026-01-20

Covariance

What is covariance?

First of all, let us remind ourselves what variance is. It is the average squared deviated from the average. It describes the spread of the data. A large variance indicates that the data is very scatter and vice-versa.

Covariance is a measure of how two random variables vary with respect to one another. It is defined very similar to variance. $\mathrm{Cov}(X, Y) = \mathrm{E}[(X - \mu_x)(Y - \mu_y)]$ Notice that if we plug in $\mathrm{Cov}(X, X)$ we get back $\mathrm{Var}(X))$