Let X and Y have joint probability density function

fX,Y(x,y) = x+y, for 0 <=x<= 1, o<=y<=1

0, otherwise

How do i go about determining the corr(X,Y)?

Could someone outline the steps please.. Any help would be appreciated..

Printable View

- October 11th 2008, 05:47 AMbrd_7Joint Probability Function
Let X and Y have joint probability density function

fX,Y(x,y) = x+y, for 0 <=x<= 1, o<=y<=1

0, otherwise

How do i go about determining the corr(X,Y)?

Could someone outline the steps please.. Any help would be appreciated.. - October 11th 2008, 01:29 PMLaurent
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. - October 11th 2008, 02:19 PMmr fantastic
- October 11th 2008, 03:25 PMbrd_7
Thanks so much, Ok this is what i got...

E[XY] = 1/3

E[X]^2 = (1/3 + y/2)^2 = y^2/4 + 2y/6 + 1/9

E[X^2] = 1/4 + y/3

E[Y] = 1/3 + x/2

And as a final answer.. i gained..

y^4/16 - 2y^3/24 - 13y^2/144 + 10y/216 + 10/324

- October 11th 2008, 03:29 PMLaurent
- October 12th 2008, 02:14 AMbrd_7
Oh right, that makes sense.. Im assuming you would do the same if i needed E(Y)?

Well as a final answer i got -1/11..

Thanks for all the help again.