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

  1. Dec 15, 2008 #1
    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

  2. jcsd
  3. Dec 17, 2008 #2
    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.

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