Gautam Sethi wrote in message <8jinln$9fu$[EMAIL PROTECTED]>...
>
>i wrote a little code in matlab that figures out the density of z = x*y
where x
>and y are both uniformly distributed. in the code i wrote, x and y are
>distributed over the same range and my results show a funky looking
triangular
>distribution with the mode/mean/median in the middle. is this correct? i
>remember reading somewhere many moons ago that the product of 2 uniforms is
>some other density (i.e. definitely something other than triangular), but
my
>memory is fuzzy and i can't seem to find that reference. any help will be
>appreciated. also, if you know anything about the density of z when x and y
>have diff supports ...
>
>best,
>gautam.
>
I think you are a victim of some confusion: your subject is "convolution"
while you talk about product. The distribution of the _convolution_ of two
Uniform(0,1) variables, that is of z=x+y is really the triangular
distribution. To find the distribution of the product, you can use the
standard formula for the pdf of a function of two variables found in many
probability textbooks. Define an auxiliary variable u=x, find the joint
distribution of x and u, then integrate out u to get the marginal
distribution of z.
Aniko
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