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

 Messages: [ Previous | Next ]
 adder Posts: 153 Registered: 10/3/07
Re: Random numbers
Posted: Dec 22, 2007 4:08 PM

On Dec 22, 12:14 pm, vr <simple.pop...@gmail.com> wrote:
> On Dec 23, 12:52 am, 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:
>
> > > > >> >> > Given a function that returns a random number between 1-5, write one
> > > > >> >> > that returns a random number between 1-7 for the case when it should
> > > > >> >> > be integer and for the case it can be real.

>
> > > > >> >> Let S be the function that generates a RN between 1 and 5. Then
>
> > > > >> >> T = S_1 + S_2 + ... + S_7
>
> > > > >> >> For the reals , RN_7 = T/7
>
> > > > >> >May be this should fix it:
>
> > > > >> >For the reals , RN_7 = 1 + (T-7)*3/14
>
> > > > >> Yes, that fixes the range.
>
> > > > >> But it's still biased (that is, not a unform distribution).
>
> > > > >> quasi- Hide quoted text -
>
> > > > >> - Show quoted text -
>
> > > > >Hmm. Let me simplify it:
>
> > > > >RN_7 = T*3/14 - 0.5
>
> > > > >If you look at T*3/14, it just scales the sum of random numbers
> > > > >uniformly using a constant multiplier. Did I miss to notice any non-
> > > > >uniformity here?

>
> > > > Yes, T is not uniformly distributed in its range.
>
> > > Ok. But if S_n is guaranted to be uniformly distributed in the range 1
> > > to 5, then doesn't it mean the sum of 7 such numbers will also get
> > > distributed over 7 to 35? I'm just curious. Thanks.

>
> > The sum is not uniformly distributed over the integers from 7 to 35.
> > Imagine for example tossing two fair dice. We are familiar with the
> > fact that the sum is not uniformly distributed over the integers from
> > 2 to 12: a sum of 2 is much less likely than a sum of 7.

>
> > 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. Let f be any function of n variables, and
> > let X = f(T_1, T_2, ..., T_n). Then X cannot be uniformly distributed
> > over the integers from 1 to 7. So 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. Some 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 (!).
>
> -vr

The observation does not hold for "the reals." In fact, almost the
opposite holds. Roughly speaking, let W be a continuously distributed
random variable, and let f be a density function. Then there is a
function g such that g(W) has density function f. So informally we
can use a suitable function of W to simulate any continuous
distribution.

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