Thread: Joint Density Problem

1. Joint Density Problem

This question's been killing me for hours.

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?

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

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 $\displaystyle xe^{-(x+y)}$ for x,y>0

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

4. Originally Posted by bzgeb
f(x, y) is equal to $\displaystyle xe^{-(x+y)}$ 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 $\displaystyle f(x,y)=xe^{-(x+y)}$, the integrals converge.

p.s. Im leaving the computation to u...if you like ill post the answers.

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

6. 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 $\displaystyle f(x,y) = xe^{(-x+y)}$. 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.

7. 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.