random variables independence I need to check if Z and W are dependent or not.
X,Y ~ Exp(2)

Then I define: Z=X-Y , W=X+Y.
Now How I can check that Z and W are dependent or not ?
I know from the teory that I should show that f(z,w) = f(z)f(w) , but I dont see how I do it here.
Thanks for help.

If $Z$ and $W$ are indeed independent then e.g. $P(Z>1,W<1)=P(Z>1)P(W<1)>0$. 
This contradicts that $P(Z<W)=1$ as mentioned in the comment of @Did.
