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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.

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    Got something from my answer?2012-09-30

1 Answers 1

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(a) Integrate the function $f_{X,Y}$ on the set $[0,1]^2$ and choose $c$ such that the result is $1$.
(b) Integrate the function $(x,y)\mapsto f_{X,Y}(x,y)$ on the set $(x,y)\in[0,1]^2$, $x\gt2y$.
(c) Integrate the functions $f_{X,Y}(x,\cdot)$ and $f_{X,Y}(\cdot,y)$.

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    What I think is that I fail to see how the integrals in this WA page are even related to your problem... You might want to read again, slowly, my last comment.2012-09-17