Let X and Y have joint probability density function
fX,Y(x,y) = x+y, for 0 <=x<= 1, o<=y<=1
How do i go about determining the corr(X,Y)?
Could someone outline the steps please.. Any help would be appreciated..
One has , right? So what you need to compute is , , , and . In fact, the pdf of is symmetric in , so that and have same distribution and the formula reduces to: .
To compute , just integrate times the pdf of (over the square ).
You can do the same with the other ones (integrating and ), but you may find it quicker to first determine the pdf of . For that, you just have to integrate the pdf of with respect to the variable , keeping fixed.