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Help with density function

  1. Sep 19, 2009 #1
    1. The problem statement, all variables and given/known data

    f(x) is a density on R+ so f(x) < 0 if x < 0. Define g_(X,Y)(x,y) = f(x+y)/(x+y). Show g is a density on R^2.

    2. Relevant equations

    the first part is easy (showing that g is in fact >= 0. The part I am struggling with is the double integral of the g(x,y) over the positive reals.


    3. The attempt at a solution

    I have tried substitution as well as by parts but I always end up with something I can't integrate. Any suggestions on how to attach the problem?


    I'm guessing I need to give more information to get a response. I am struggling getting going on the actual problem...I believe the substition i used (u = x+y) is wrong as I get a very nasty integral. I am just looking for some advice on how to get going
     
    Last edited: Sep 19, 2009
  2. jcsd
  3. Sep 20, 2009 #2
    Welcome to PF, jam_33.

    I would try converting to polar coordinates.
     
  4. Sep 20, 2009 #3
    Hello Billy Bob,

    Thanks for the suggestion as it worked!

    cheers,

    jam_33
     
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