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Math Help - Joint Density Problem

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by bzgeb View Post
    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 xe^{-(x+y)} for x,y>0
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  3. #3
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    Quote Originally Posted by vince View Post
    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.
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  4. #4
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    Quote Originally Posted by bzgeb View Post
    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.
    Last edited by vince; February 21st 2010 at 10:03 AM. Reason: added the p.s.
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  5. #5
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    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.
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  6. #6
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    Quote Originally Posted by bzgeb View Post
    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.
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  7. #7
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    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.
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