In article <8jjpch$dr4$[EMAIL PROTECTED]>,
Gautam Sethi <[EMAIL PROTECTED]> wrote:
>Herman Rubin <[EMAIL PROTECTED]> wrote:
>: In article <002a01bfe2f1$5548e6e0$[EMAIL PROTECTED]>,
>: David A. Heiser <[EMAIL PROTECTED]> wrote:
>:>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.
>thanks herman. i was able to derive the convolution pretty easily. however,
>the product seems a lot harder. is the product easy to figure out too? any
>tips and tricks i should know? someone suggested that the density of z = x*y
>is -log(x) if both x and y have the support [0,1]. is this correct?
If an endpoint is zero, scaling reduces it to (0,1).
It is not hard to prove in many ways that the density
of the product of k independent uniform (0,1) random
variables is (-ln(x))^{k-1}/(k-1)!.
--
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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