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Distribution of xy/z. X,y,z ind uniform 0 to 1

  1. Jan 2, 2012 #1
    Hi,

    Can someone please help me solve the following:

    Find the distribution of xy/z where x, y, z is independent and uniformly distributed from 0 to 1


    Thanks for the help
     
  2. jcsd
  3. Jan 2, 2012 #2

    chiro

    User Avatar
    Science Advisor

    Hey Nubyra and welcome to the forums.

    Although I can't give you an analytic answer off the top of my head, one suggestion I do want to make is to use monte-carlo simulation to get a good idea of what the distribution should look like.

    Most statistical problems will be able to simulate uniform by default so you should have no problems with this. I would recommend you use R since it is free, well documented, and is easy to use for this task.

    http://www.r-project.org
     
  4. Jan 3, 2012 #3
    If you know the distribution functions you might be able to obtain the product[itex]f_1(x)f_2(y)f_3^{-1}( z)[/itex] analytically.

    http://en.wikipedia.org/wiki/Inverse_transform_sampling

    http://mathworld.wolfram.com/UniformProductDistribution.html

    http://mathworld.wolfram.com/InverseGaussianDistribution.html

    http://mathworld.wolfram.com/NormalProductDistribution.html

    EDIT: Most distributions can be restated in terms the Gaussian based on the sampling distribution and the Central Limit Theorem.
     
    Last edited: Jan 3, 2012
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