Solving for the covariance of a joint pdf Let X and Y have a joint pdf given by  
$f_{x,y}(x,y) =
\begin{cases} 1 & \text{if } 0<y<1,\text{ } y-1<x<1-y \\ 0 & \text{otherwise} \end{cases}$.  
(a) Find Cov(X,Y) and Corr(X,Y). Are X and Y independent?
(b) Find Cov(|X|,|Y|) and Corr(|X|,|Y|).
(c) Find Cov(3|X|, 4|Y|) and Corr(3|X|, 4|Y|).
(d) Find Var(3X - 2Y).  
So I know Covariance is E(XY)-E(X)E(Y). And since this is the indicator function, E(XY) should be 1*P(0 < y < 1, y-1 < x < 1-y) + 0*P(otherwise), which is just P(0 < y < 1, y-1 < x < 1-y). From here, I'm not sure if I take the double integral of this function with parameters listed above, or if I am taking the wrong approach. Not sure how to calculate E(X) or E(Y) either. Once I figure this part out, how absolute values will play a role?

Random variables $(X,Y)$ have joint pdf $f(x,y)$:

(source: tri.org.au) 
Here is a plot of the pdf, which is helpful in understanding the domain of support:

(source: tri.org.au) 
The rest of the problem (parts a to d) can easily be solved using a computer algebra system. I am using the mathStatica add-on to Mathematica to do the grunt work for me (I am one of the authors of the former). I don't believe in answering homework problems, so here is the answer to only one part of each question. Presumably you will need to show your working anyway (which Andre has kindly provided detailed help on) ... and the output below will give you something to aim towards ...

(source: tri.org.au) 
