**Covariance** is a measure of the linear dependence of two 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 and respectively, is as follows:

where E is the operator for the expectation.

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.