Question

Q. 4. Find the correlation coefficient between x and y

Answer 1

The covariance of X and Y neccessarily reflects the units of both random variables.  It is helpful instead to have a dimensionless measure of dependency, such as the correlation coefficient does.

Definition.  Let X and Y be any two random variables (discrete or continuous!) with standard deviations σX and σY, respectively. The correlation coefficient of X and Y, denoted Corr(X,Y)or  (the greek letter "rho") is defined as: 

ρXY=Corr(X,Y)=Cov(X,Y)σXσY=σXYσXσYρXY=Corr(X,Y)=Cov(X,Y)σXσY=σXYσXσY