Given the pdf of two variable, find the distribution of the function

[xuxiaolichina]

Hi all,

I am new here. I have a problem about statistics:

now I have two variable a & b, both of them are uniformly distributed in [-1 1], I want to find the pdf of the function f=|a-b|/|a+b|.

Any hint is welcome, thanks a lot

xiaoli

 

[Enuma_Elish]

I would first picture the domain of f. You know (a , b) is distributed over a square S on the Cartesian plane with vertices (corners) at (-1,-1), (-1,1), (1,1) and (1,-1). How does f "look" like over that square? What are the boundaries on f? Let's say L < f < U over S. The next question is, are there any "jump points" between L and U such that the distribution of f is discontinuous at these points? Next, are there any "lump points" such that the distribution of f is "lumpy" at these points? Finally, you'll need to compute the distribution of f between successive jump-or-lump points using the distributions of a and b.

EnumaElish