Thanks mate :)
So using the alternate definition, I got:
Cov(X,Y) = 24 \int^{1}_{0}\int^{1-y}_{0}(x-\frac{2}{5})(y-\frac{2}{5})xydxdy
= 24 \int^{1}_{0}\int^{1-y}_{0}x^{2}y^{2}-\frac{2x^{2}y}{5}-\frac{2xy^{2}}{5}+\frac{4xy}{25}dxdy
=24\int^{1}_{0}\frac{-1}{75}(2-5y)^{2}(y-1)^{2}ydy...
The following question appeared on a practice exam:
For
f(x,y) = 24xy if 0<x+y<1 , 0<x,y
0 elsewhere
find Cov(X,Y)
I used Cov(X,Y) = E(XY) - E(X)E(Y) to calculate covariance, with
E(XY) = \int^{1}_{0}\int^{1-y}_{0}24x^{2}y^{2}dxdy
but for some reason I didn't get the...