Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    xiaoli
     
  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.

    EnumaElish
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?