# X and Y Joint Density Question - Compute the Density of X and Y

I simply cannot understand this. My TAs aren't available until tomorrow and I really do not want to put this off until then. I'd like to have some idea of how to do this beforehand.

The question is:

The joint density function of X and Y is

f(x, y) =

2
for 0 < x < y, 0 < y < 1

0 otherwise

a) Compute the density of X. b) Compute the density of Y. c) Are X and Y independent?

Integrals have something to do with this, I know, but I'm not sure how to use them to get the answers I want. Independence in terms of probability I know but I don't know how to apply it to this problem.

TLDR: I need an explanation (thorough, please) on how to approach this problem so I know how to complete it and obtain the correct answer.

• If you are "integrating out" $x$, then indeed $x$ goes from $0$ to $y$. If you are integrating out $y$, then $y$ goes from $x$ to $1$. I think the best way to see this is to draw a picture. The joint density "lives" on the triangle with vertices $(0,0)$, $(1,1)$, and $(0,1)$. Draw that triangle. – André Nicolas Apr 27 '15 at 23:12