<P> A distinction must be made between (1) the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and (2) the sample covariance, which in addition to serving as a descriptor of the sample, also serves as an estimated value of the population parameter . </P> <P> The covariance between two jointly distributed real - valued random variables X and Y with finite second moments is defined as the expected product of their deviations from their individual expected values: </P> <Dl> <Dd> cov ⁡ (X, Y) = E ⁡ ((X − E ⁡ (X)) (Y − E ⁡ (Y))), (\ displaystyle \ operatorname (cov) (X, Y) = \ operatorname (E) ((\ big () (X - \ operatorname (E) (X)) (Y - \ operatorname (E) (Y)) (\ big))),) </Dd> </Dl> <Dd> cov ⁡ (X, Y) = E ⁡ ((X − E ⁡ (X)) (Y − E ⁡ (Y))), (\ displaystyle \ operatorname (cov) (X, Y) = \ operatorname (E) ((\ big () (X - \ operatorname (E) (X)) (Y - \ operatorname (E) (Y)) (\ big))),) </Dd>

In particular how does the notion of variance provide a special case for the concept of covariance