Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 simple.popeye@gmail.com Posts: 38 Registered: 12/18/07
Re: Random numbers
Posted: Dec 23, 2007 7:43 AM

On Dec 23, 5:32 pm, vr <simple.pop...@gmail.com> wrote:
> On Dec 23, 5:15 pm, vr <simple.pop...@gmail.com> wrote:
>
>
>
>
>

> > On Dec 23, 2:03 am, quasi <qu...@null.set> wrote:
>
> > > On Sat, 22 Dec 2007 11:17:53 -0800 (PST), vr <simple.pop...@gmail.com>
> > > wrote:

>
> > > >On Dec 23, 12:00 am, quasi <qu...@null.set> wrote:
> > > >> On Sat, 22 Dec 2007 13:51:57 -0500, quasi <qu...@null.set> wrote:
> > > >> >On Sat, 22 Dec 2007 10:43:27 -0800 (PST), 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.

>
> > > >> >Yes, but not uniformly.
>
> > > >> >What's the chance of getting exactly 35?
>
> > > >> >If it was a uniform distribution it would be 1/29, right?
>
> > > >> Of course, that's assuming S is a uniformly distributed integer
> > > >> variable on {1,2,3,4,5}.

>
> > > >> If instead, S is a uniformly distributed continuous variable on (1,5)
> > > >> then we can ask -- what's that chance of getting a result more than
> > > >> 34? It should be at least 1/28, right? But it's easily seen to be a
> > > >> lot less than that (the probability is bounded above by  1/2^(14)).

>
> > > >I understand the problem with the intger sum. But for the sum of
> > > >reals, If there is a non-uniformity I think it is due to finite number
> > > >of double precision numbers available in the given interval.

>
> > > No, nothing to do with that.
>
> > > Assume S is a true continuous, random number generator, with uniform
> > > distribution (1,5).

>
> > > But T is the _sum_ of 7 independently generated values of S.  While
> > > its range is (7,35), it is definitely not uniformly distributed. The
> > > bias is towards the mean (21), and away from the ends (7 and 35).

>
> > > If T was uniformly distributed, the probability of T > 34 would be
> > > exactly 1/28. However the only way T can exceed 34 is if all of the 7
> > > generated S values exceed 4 (a necessary but not sufficient
> > > condition).

>
> > > But in fact, since the probability that an S value exceeds 4 is 1/4,
> > > the probability that T exceeds 34 must be less than (1/4)^7, or
> > > 1/2^(14).

>
> > But if you consider that probability that an S value exceeds (4 + 6/7)
> > is 1/28. And any value of S exceeding (4 + 6/7) results in T value
> > exceeding 34, isn't it?

>
> Correction: The probablity for all 7 values of S for exceeding (4 +
> 6/7) is 1/(28^7). And this probability should be same for any 1/28
> segment in the range [1,5]. Is this correct?

Hmm - but there are too many combinatins summing up to other 27
segments of the [7,35], while the segment [34,35] has only
combination, so the probablities are not equal. Yep! The distribution
is not uniform :) Sorry , I was bit slow on these. And this is my last
post on this topic. Thanks.

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