1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2|

  1. Oct 25, 2009 #1
    Hi guys!

    1. The problem statement, all variables and given/known data

    Do you know how to get the cdf and pdf of the absolute difference of two iid standard uniform X1 and X2 : X = |X1 − X2| ?

    2. Relevant equations

    Come across http://en.wikipedia.org/wiki/Triang...difference_of_two_standard_uniform_variables" we know that the cdf is 2x - x2 and the pdf is 2 -2x.
    How do we get/prove it?


    Thank you very much!
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Oct 25, 2009 #2
    Re: cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2

    3. The attempt at a solution

    Is it solvable using the joint pdf ? Still trying various boundaries for the integral... kinda stuck there... please help ... T_T
    [tex] F_{X}(x) = \int \int_{|x_{1}-x_{2}|\leq x} f_{x_{1}}(x_{1}) f_{x_{2}}(x_{2}) dx_{1}dx_{2}[/tex]
     
  4. Oct 25, 2009 #3
    Re: cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2

    *bump*
     
  5. Oct 26, 2009 #4
    Re: cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2

    Yes, this is the way to do it. I'll use different variables to simplify notation. X is uniform on [0,1], and so is Y.

    Fix t. Find P(|X-Y|<t). Draw the region {(x,y) : |x - y| < t}. Intersect it with the unit square [0,1] x [0,1]. The shape of the resulting region depends on t. For the interesting (i.e. nontrivial) values of t, you get a hexagon.

    Since f_X(x) and f_Y(y) are constants, the "integration" can be done simply by using elementary geometry formulas (e.g. area of square, area of triangle).
     
  6. Oct 26, 2009 #5
    Re: cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2

    Thanks for the reply.

    Umm... what would be the boundaries/intervals in the first and second integral ?
     
  7. Oct 27, 2009 #6
    Re: cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2

    *bump*

    Anyone interested in solving this problem, please dont hesitate,

    still waiting ... :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2|
Loading...