Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Random numbers
Replies: 64   Last Post: Dec 24, 2007 1:04 PM

 Messages: [ Previous | Next ]
 Herman Rubin Posts: 6,721 Registered: 12/4/04
Re: Random numbers
Posted: Dec 22, 2007 8:51 PM

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
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@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558

Date Subject Author
12/21/07 Champ
12/21/07 quasi
12/21/07 quasi
12/21/07 Phil Carmody
12/21/07 quasi
12/21/07 quasi
12/21/07 Phil Carmody
12/21/07 quasi
12/21/07 Phil Carmody
12/21/07 Phil Carmody
12/21/07 quasi
12/21/07 quasi
12/21/07 Phil Carmody
12/21/07 quasi
12/21/07 Phil Carmody
12/21/07 Phil Carmody
12/21/07 quasi
12/21/07 Phil Carmody
12/21/07 quasi
12/21/07 Marshall
12/21/07 Phil Carmody
12/21/07 quasi
12/21/07 Phil Carmody
12/21/07 Marshall
12/21/07 briggs@encompasserve.org
12/21/07 William Elliot
12/21/07 quasi
12/22/07 William Elliot
12/21/07 Pubkeybreaker
12/21/07 b92057@yahoo.com
12/22/07 quasi
12/21/07 simple.popeye@gmail.com
12/21/07 simple.popeye@gmail.com
12/22/07 quasi
12/22/07 Gib Bogle
12/22/07 quasi
12/21/07 Marshall
12/22/07 simple.popeye@gmail.com
12/22/07 quasi
12/22/07 simple.popeye@gmail.com
12/22/07 quasi
12/22/07 quasi
12/22/07 quasi
12/22/07 simple.popeye@gmail.com
12/22/07 quasi
12/23/07 simple.popeye@gmail.com
12/23/07 simple.popeye@gmail.com
12/23/07 simple.popeye@gmail.com
12/23/07 simple.popeye@gmail.com
12/23/07 simple.popeye@gmail.com
12/22/07 simple.popeye@gmail.com
12/22/07 Herman Rubin
12/22/07 b92057@yahoo.com
12/22/07 quasi
12/23/07 b92057@yahoo.com
12/23/07 quasi
12/23/07 b92057@yahoo.com
12/24/07 quasi
12/24/07 quasi