Difference between revisions of "Covariance"
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'''Covariance''' is a measure of the linear dependence of two [[variable]]s. 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''' is a measure of the linear dependence of two [[variable]]s. 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 | + | 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> | : <math>\operatorname{Cov}(X, Y) = \operatorname{E}[(X - \mu) (Y - \nu)], \,</math> | ||
| − | where E is the operator for the [[expectation]]. | + | where E is the operator for the [[expectation (math)|expectation]]. |
If ''X'' and ''Y'' are completely [[statistically independent]] from each other, then they have zero covariance. | If ''X'' and ''Y'' are completely [[statistically independent]] from each other, then they have zero covariance. | ||
Revision as of 01:01, February 22, 2009
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.
