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

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The discussion focuses on finding the distribution of the expression xy/z, where x, y, and z are independent variables uniformly distributed between 0 and 1. A Monte Carlo simulation is recommended as an effective method to approximate this distribution, with R being the suggested tool due to its accessibility and robust documentation. The conversation also references the potential for analytic solutions using distribution functions and highlights the relevance of the Central Limit Theorem in restating distributions in terms of Gaussian distributions.

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Nubyra
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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
 
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Nubyra said:
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

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
 
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.
 
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