Definition:Covariance

Definition

Let $X$ and $Y$ be random variables.

Let $\mu_X = \expect X$ and $\mu_Y = \expect Y$, the expectations of $X$ and $Y$ respectively, exist and be finite.

Then the covariance of $X$ and $Y$ is defined by:

$\cov {X, Y} = \expect {\paren {X - \mu_X} \paren {Y - \mu_Y} }$

where this expectation exists.

Also see

• Definition:Autocovariance

• Results about covariance can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): covariance
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): moment
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): covariance
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): moment
• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $4.6$: Covariance and Correlation: Definition $4.6.1$