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

 Messages: [ Previous | Next ]
 b92057@yahoo.com Posts: 1,187 Registered: 4/18/05
Re: Random numbers
Posted: Dec 23, 2007 7:06 PM

On Dec 22, 5:25 pm, quasi <qu...@null.set> wrote:
> On Sat, 22 Dec 2007 16:30:20 -0800 (PST), bill <b92...@yahoo.com>
> wrote:
>
>
>

> >On Dec 22, 10:16 am, 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
>
> >The OP does not specify a uniform
> >distribution, merely the range.

>
> This has already been discussed.
>
> The obvious assumption _implicit_ in the problem, even if not unstated
> is that the resulting distribution should be uniform. Of course, it
> should have been specified, but common sense dictates that in the
> absence of the required info, to choose the natural default.
>
> If there was no preference for a distribution, there would be no need
> to use the RNG provided for the range 1 to 5. We could just always
> produce the number 3, for example. In other words, the very fact that
> an RNG for the range 1 to 5 was given as part of the problem makes it
> clear that the for the actual problem (not the OP's deficient
> statement of it), it almost certainly _was_ specified that the
> required distribution should be uniform.
>
>
>

> >RN_7 = T/7 satisfies the range 1 thru 7.
>
> So what? It's badly biased. Worse, since there is no discussion of
> bias or the lack of it, it's misleading to those unaware of the issue.
>

> >T/7 is a numner in the range 1 thru 7,
> >but is it random?

>
> Ok, but note that T/7 never exceeds 5.
>
> It's definitely not uniformly random.
>

> >If RN_7 = T mod 7 +1, the probability
> >of a correct guess is 1/7

>
> Nonsense. Do a simulation.
>

> >If RN_7 = T/7, the probability
> >of a correct guess is < .11 if you always
> >guess that T = 21 or 22

>
> If the original RNG is uniformly distributed on the interval (1,5),
> then it's a continuous distribution, so the probability that T = 21 or
> T = 22 is 0.

That makes it even harder to guess correctly if you have to be exact.

>
> And once again, since T/7 only has range 1 to 5, thus it's obviously
> not uniform on (1,7). It's not even uniform on (1,5), since it has
> more concentration near the mean (3) than near the ends.
>
> quasi

Assume that RNG_5 is continuous in the interval 1 - 5 and 0
elsewhere.,
Let X_i be a number generated by RNG_5. Then Y_i = 1.5 * (X_i) -
0.5 is
continuous in the interval 1 - 7 and 0 elsewhere.

That is, unless there are more points between 1 and 7 than there are
between
1 and 5?

Bill J

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