# Joint Probability Density Function [closed]

I've been trying to solve this question on joint probability. I have problem mainly because I keep getting the denominator that scales up to infinity. I understand that y can be infinitely small to offset. But I am unsure how this can be done. Anyone can help me out on this? Thanks!!

The joint density function of X and Y is given by

f(x,y) = (15x/2) (2-x-y) for x>0, y<1 and 0 otherwise

Find f(x|y).

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For example, the joint density is negative at x=3, y=0? – Did Aug 21 '12 at 9:36
If you took f(x|y) = f(x,y)/fy(y) Where fy(y) = integrate (15x/2)(2-x-y) dx from 0 to infinity, I get some cubic equation of x and y. But since x scales up to infinity I am not sure how to solve it. – Ken Ryou Aug 21 '12 at 9:37
It is not a joint density. The area under the joint density should be 1. – Seyhmus Güngören Aug 21 '12 at 9:40
How did you determine that? do you mind showing your working? Because if I integrate wrt x, I can't get a meaningful results to integrate wrt to y... – Ken Ryou Aug 21 '12 at 9:42
I do now know, what is worse: a negative density, or an undefined one - but anyway, your density is undefined in the point $(2,0)$ where it can be either $+\infty$ (provided density is allowed to be infinite) or $-\infty$ depending on the direction you approach the point. – Ilya Aug 21 '12 at 10:15