Correlation

Definition

• For RV $X$ with Mean ${\mu }_x=E(X)$ and Variance ${\sigma }_X^2=V(X)$
• For RV $Y$ with Mean ${\mu }_Y=E(Y)$ and Variance ${\sigma }_Y^2=V(Y)$
• The correlation of $X$ and $Y$ defined as $Corr(X,Y)=\frac{Cov(X,Y)}{{\sigma }_X{\sigma }_Y}=\frac{Cov(X,Y)}{\sqrt{V(X)V(Y)}}$, $p_{X,Y}\in [-1,1]$