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

1. Jan 2, 2012

### Nubyra

Hi,

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

Thanks for the help

2. Jan 2, 2012

### chiro

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

3. Jan 3, 2012

### SW VandeCarr

If you know the distribution functions you might be able to obtain the product$f_1(x)f_2(y)f_3^{-1}( z)$ 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