Definition:Covariance
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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
- 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 $4.6.1$