Covariance

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.