# Joint Density Problem

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• Feb 21st 2010, 06:56 AM
bzgeb
Joint Density Problem
This question's been killing me for hours.

http://users.encs.concordia.ca/~b_zgeb/problem12.png

My assumption is that when they ask for the density of X they're asking for the marginal density function f(x). In this case you would take the integral of f(x,y) over all values of y, or in other words, the integral of f(x,y) from 0 to infinity. However, when I do this it becomes infinity. The same goes for trying to compute the density of Y.

Could somebody show me what I'm doing wrong?
• Feb 21st 2010, 07:39 AM
vince
Quote:

Originally Posted by bzgeb
This question's been killing me for hours.

http://users.encs.concordia.ca/~b_zgeb/problem12.png

My assumption is that when they ask for the density of X they're asking for the marginal density function f(x). In this case you would take the integral of f(x,y) over all values of y, or in other words, the integral of f(x,y) from 0 to infinity. However, when I do this it becomes infinity. The same goes for trying to compute the density of Y.

Could somebody show me what I'm doing wrong?

are u sure f(x,y) is not equal to $xe^{-(x+y)}$ for x,y>0
• Feb 21st 2010, 08:19 AM
bzgeb
Quote:

Originally Posted by vince
are u sure f(x,y) is not equal to $xe^{-(x+y)}$ for x,y>0

f(x, y) is equal to $xe^{-(x+y)}$ for x,y>0. The problem is: when I try to find the density of X I take the definite integral of f(x,y) dy from 0 to infinity. If you try to do that you'll find that it simply becomes infinity.
• Feb 21st 2010, 08:49 AM
vince
Quote:

Originally Posted by bzgeb
f(x, y) is equal to $xe^{-(x+y)}$ for x,y>0. The problem is: when I try to find the density of X I take the definite integral of f(x,y) dy from 0 to infinity. If you try to do that you'll find that it simply becomes infinity.

that's not what you wrote...check your first post. with $f(x,y)=xe^{-(x+y)}$, the integrals converge.

p.s. Im leaving the computation to u...if you like ill post the answers.
• Feb 21st 2010, 09:31 AM
bzgeb
This is embarrassing, I'm sorry I misread your reply. I took a screenshot of the assignment directly so it's definitely $f(x,y) = xe^{(-x+y)}$. However, now that you bring that up I'm starting to wonder if there's a typo in the assignment.
• Feb 21st 2010, 09:39 AM
vince
Quote:

Originally Posted by bzgeb
This is embarrassing, I'm sorry I misread your reply. I took a screenshot of the assignment directly so it's definitely $f(x,y) = xe^{(-x+y)}$. However, now that you bring that up I'm starting to wonder if there's a typo in the assignment.

i think so...the marginal denisty of X is undefined otherwise.
• Feb 21st 2010, 09:54 AM
bzgeb
I emailed my professor so I should find out soon. Thanks for taking a look at my problem and confirming that I wasn't doing something wrong.