Re: Product of distribution

On Jan 2, 7:17 am, John <iamach...@xxxxxxxxx> wrote:
Is the product of two uniform distribution uniform ?

No. If X and Y are two independent non-negative rvs with pdfs
(probability density functions) f(x) and g(y), respectively, the pdf
h(z) of Z = X*Y is given by h(z) = integral(1/y * f(y) *g(z/y) dy,
y=0..infinity). In particular, if X and Y are uniform(0,1) we have
h(z) = integral(1/y * 1{0 < y < 1}*1{0 < z/y < 1} dy ,y>=0) =
integral( 1/y, y=z..1) = -ln(z), for 0 < z < 1, and h(z) = 0 for z < 0
or z > 1. Note that integral(-ln(z), z=0..1) = 1, as it should.

R.G. Vickson
.

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