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

In summary, the conversation discusses finding the distribution of xy/z where x, y, z are independent and uniformly distributed from 0 to 1. One suggestion is to use monte-carlo simulation in R to get an idea of the distribution, and if the distribution functions are known, they can be obtained analytically. The use of the Gaussian distribution and the Central Limit Theorem is also mentioned.
  • #1
Nubyra
1
0
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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  • #2
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
 
  • #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:

1. What is the distribution of xy/z?

The distribution of xy/z refers to the probability distribution of the ratio of two independent random variables x and y divided by a third independent random variable z, all of which are uniformly distributed between 0 and 1.

2. How is the distribution of xy/z calculated?

The distribution of xy/z can be calculated by taking the ratio of the joint probability density function of x and y to the probability density function of z. This can be represented as P(xy/z) = P(x,y)/P(z).

3. What is the expected value of the distribution of xy/z?

The expected value, or mean, of the distribution of xy/z is equal to 1/2, as this is the expected value of each individual variable (x, y, and z) in the uniform distribution between 0 and 1.

4. Is the distribution of xy/z symmetric?

No, the distribution of xy/z is not symmetric. It is skewed to the right, as values close to 0 for x and y will result in a larger overall value for xy/z.

5. How can the distribution of xy/z be used in scientific research?

The distribution of xy/z can be used in various statistical analyses and simulations to model real-world scenarios, such as the distribution of resource allocation among different groups or the distribution of reaction rates in chemical reactions.

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