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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
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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
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closed as not a real question by Did, Nate Eldredge, Sasha, William, t.b. Sep 11 '12 at 16:14

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

1 Answer

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But how do u show that it is not a pdf? Because like ken mention I too can't even show it is not a pdf because the first integral is giving me problem as well

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Obviously, you did not read my two comments (not to mention others). – Did Aug 23 '12 at 21:32

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