Re: Random numbers
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 22 Dec 2007 20:51:52 -0500
In article <1ae23332-0aac-4834-ad14-0372c6da53e5@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
vr <simple.popeye@xxxxxxxxx> wrote:
On Dec 23, 12:52=A0am, no comment <adler.m...@xxxxxxxxx> wrote:
On Dec 22, 10:43 am, vr <simple.pop...@xxxxxxxxx> wrote:
On Dec 22, 11:35 pm, quasi <qu...@xxxxxxxx> wrote:
On Sat, 22 Dec 2007 10:32:37 -0800 (PST), vr <simple.pop...@xxxxxxxxx>=
wrote:
On Dec 22, 11:16 pm, quasi <qu...@xxxxxxxx> wrote:
On Fri, 21 Dec 2007 10:57:00 -0800 (PST), simple.pop...@xxxxxxxxx
wrote:
On Dec 21, 11:37 pm, bill <b92...@xxxxxxxxx> wrote:
On Dec 21, 3:16 am, John <iamach...@xxxxxxxxx> wrote:
.....................
In general, let n be a fixed positive integer, and let T_1, T_2, ...,
T_n be independent reandom variables, each uniformly distributed oover
the integers from 1 to 5. =A0Let f be any function of n variables, and
let X =3D f(T_1, T_2, ..., T_n). =A0Then X cannot be uniformly distributed=
over the integers from 1 to 7. =A0So any algorithm to produce a random
variable uniformly distributed over the integers from 1 to 7 from
independent random variables uniformly distributed over the integers
from 1 to 5 must use a "variable" n. =A0Some of the algorithms that have
been proposed above do indeed use such a variable n, and work.
Got it. Is this applicable only for finite possibilities such as an
integer interval? or is it valid for reals too? I think not, because
any specific real number has zero chance of getting hit, but we still
get some random real numbers (!).
Which theorem is being considered? From discrete, one can
only get discrete. If one has a random variable with
probabilities 1/2, 1/2^2, 1/2^3, etc, one can get any
discrete distribution with k alternatives using at most
k-1 independent random variables.
If the original random variable can take on real values,
the results are quite different. Given any random variable
X with a purely non-atomic distribution on a Polish space,
and any probability distribution m on a Polish space (no
restriction), there is a function f such that f(X) has the
distribution m.
--
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, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
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