The **correlation** between r.v.s $X$ and $Y$ is

given that both variances are greater than zero.

## Properties

Location-scale transformations do not affect correlations, as long as we don’t multiply the variables by zero. So, we have $Corr(aX+b,cY+d)=Corr(X,Y)$ for $a>0,c>0$.

This implies correlation does not depend on units of measurement.

It must be true that $−1≤Corr(X,Y)≤1$. A *perfect correlation* is given by $∣Corr(X,Y)∣=1$ and signifies a completely linear relationship between $X$ and $Y$.