Changes

'''Covariance''' measures how much two [[random variables]] vary together relative to each other. 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.

'''Covariance''' measures how much two [[random variable]]s vary together relative to each other. 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 value]]s <math>\mu</math> and <math>\nu</math> respectively, is as follows:

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

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

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

where E is the operator for the [[expected value]].  

where E is the operator for the expected value.  

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

If ''X'' and ''Y'' are completely [[independent variables|independent]] from each other, then they have zero covariance.

 

Note that if ''X'' and ''Y'' have covariance zero, they are un[[correlated]] but are not necessarily independent.

[[category:probability and Statistics]]

[[category:probability and Statistics]]