Difference between revisions of "Covariance"
Jump to navigation
Jump to search
m (wikilinks) |
m |
||
| Line 1: | Line 1: | ||
| − | '''Covariance''' | + | '''Covariance''' is a measure of the linear dependence of two [[random 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 [[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: | ||
Revision as of 13:18, 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 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.