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Uniform Product Distribution

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UniformProductDistribution

The distribution of the product X_1X_2...X_n of n uniform variates on the interval [0,1] can be found directly as

P_(X_1...X_n)(u)=intint...int_()_(n)delta(x_1x_2...x_n-u)dx_1dx_2...dx_n
(1)
=((-1)^(n-1))/((n-1)!)(lnu)^(n-1),
(2)

where delta(x) is a delta function. The distributions are plotted above for n=2 (red), n=3 (yellow), and so on.

See also

Uniform Difference Distribution, Uniform Distribution, Uniform Ratio Distribution, Uniform Sum Distribution

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Cite this as:

Weisstein, Eric W. "Uniform Product Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UniformProductDistribution.html

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