Difference between revisions of "Covariance"
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| − | '''Covariance''' measures how much two [[random | + | '''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 | + | 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 | + | 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]] | ||
Revision as of 20:22, July 1, 2008
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.
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 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.