
Re: Random numbers
Posted:
Dec 22, 2007 8:51 PM


In article <1ae233320aac4834ad140372c6da53e5@l6g2000prm.googlegroups.com>, vr <simple.popeye@gmail.com> wrote: >On Dec 23, 12:52=A0am, no comment <adler.m...@gmail.com> wrote: >> On Dec 22, 10:43 am, vr <simple.pop...@gmail.com> wrote:
>> > On Dec 22, 11:35 pm, quasi <qu...@null.set> wrote:
>> > > On Sat, 22 Dec 2007 10:32:37 0800 (PST), vr <simple.pop...@gmail.com>=
>> > > wrote:
>> > > >On Dec 22, 11:16 pm, quasi <qu...@null.set> wrote: >> > > >> On Fri, 21 Dec 2007 10:57:00 0800 (PST), simple.pop...@gmail.com >> > > >> wrote:
>> > > >> >On Dec 21, 11:37 pm, bill <b92...@yahoo.com> wrote: >> > > >> >> On Dec 21, 3:16 am, John <iamach...@gmail.com> 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 k1 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 nonatomic 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@stat.purdue.edu Phone: (765)4946054 FAX: (765)4940558

