Difference between revisions of "Covariance"
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: <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 | + | 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 un[[correlated]] but are not necessarily independent. | 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]] | ||
Revision as of 14:45, January 17, 2009
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.