Covariance

Covariance is a measure of the linear dependence of two random variables. If two variables tend to vary in the same direction, then they have a positive covariance. If they tend to vary in opposite directions, then they have a negative covariance.

The covariance between two random variables X and Y, having expected values <math>\mu</math> and <math>\nu</math> respectively, is as follows:

<math>\operatorname{Cov}(X, Y) = \operatorname{E}[(X - \mu) (Y - \nu)], \,</math>

where E is the operator for the expected value.

If X and Y are completely statistically independent from each other, then they have zero covariance.

Note that if X and Y have covariance zero, they are uncorrelated but are not necessarily independent.