In article <002a01bfe2f1$5548e6e0$[EMAIL PROTECTED]>,
David A. Heiser <[EMAIL PROTECTED]> wrote:
>From: Gautam Sethi <[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.
>......................
>The product and convolution are two different things. The product gives a
>triangular distribution. If I remember correctly, the distribution is
>triangular even if the two have different supports. I never tried out the
>convolution.
The convolution is the distribution of the sum; the product
has a quite different distribution.
The distribution of the sum for different ranges is a symmetric
trapezoid, with the central part having the density of the one
with larger range and length the difference of the ranges. If
the ranges are equal, this becomes a triangle; proof left to
the reader.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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