Suppose I have the following joint pdf of $X$ and $Y$.
$f_{X,Y}(x,y) = \begin{cases}c\cdot x \cdot \max(x,y) \text{ if } 0\leq x\leq 1, 0\leq y\leq 1\text{ and }x+y\leq 1;\\ 0 \text{ otherwise}\end{cases}$
How do I
(a) find the constant $c$,
(b) compute $P(X>2Y)$, and
(c) compute the marginal pdfs of $X$ and $Y$?
Currently, I have the following. For part (a), I calculated this. Is this right?
I apologize for not being able to write in the proper notation on this site. For part (b), I calculated this. Is this right?
What is part (c)? How should I set up the integrals? I am having trouble getting them to equal 1.