# Help with density function

1. Sep 19, 2009

### jam_33

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. Sep 20, 2009

### Billy Bob

Welcome to PF, jam_33.

I would try converting to polar coordinates.

3. Sep 20, 2009

### jam_33

Hello Billy Bob,

Thanks for the suggestion as it worked!

cheers,

jam_33