I got this question here and I have trouble just to start.

Consider the random variables $\displaystyle (X,Y)$ which is uniformly distributed over the triangle $\displaystyle T=\{(x,y): x>0, y>0, x+y<9\}$.

(a)Write down $\displaystyle f_{(X,Y)}{(x,y)}$, the disjoint probability density function of $\displaystyle (X,Y)$, and indicate on a graph the triangle $\displaystyle T$ where it is non-zero.

(b)Explain why X and Y are dependent (no calculations should be required)

I'm having trouble from the start to write down disjoint probability density function. I can surely draw the graph and see the triangle area, but how do I get density function? Can anyone please help me?