\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \)

Covariance

Covariance is a real that gives some sense of how much two variables are linearly related to each other, as well as the scale of these variables. Covariance is a function of a probability space and two random variables. Let \( (\Omega, \mathrm{F}, \mathbb{P}) \) be a discrete probability space let \( X: \Omega \to S_x \) and \( Y : \Omega \to S_y \), be two random variables, where \( S_x\) and \( S_y \) are finite subsets of \( \mathbb{R} \). Then the covariance of \( X \) and \( Y \) is: