Difference between revisions of "Covariance"
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| − | '''Covariance''' is a measure of the linear dependence of two [[ | + | '''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 [[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: | ||
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where E is the operator for the [[expected value]]. | 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. | + | 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 14:46, January 17, 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 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.
