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

 Messages: [ Previous | Next ]
 quasi Posts: 12,067 Registered: 7/15/05
Re: Random numbers
Posted: Dec 24, 2007 2:14 AM

On Sun, 23 Dec 2007 22:32:06 -0800 (PST), no comment

>On Dec 23, 9:32 pm, quasi <qu...@null.set> wrote:
>> On Mon, 24 Dec 2007 00:10:57 -0500, quasi <qu...@null.set> wrote:
>> >On Sun, 23 Dec 2007 19:46:21 -0800 (PST), bill <b92...@yahoo.com>
>> >wrote:

>>
>> >>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.
>>
>> >Ok, for the above, I must apologize. For the _integer_ case, the
>> >calculation (T mod 7) + 1 does appear to give a uniform distribution

>>
>> Hehe -- I take back part of my apology. It _is_ biased, but only
>> slightly.
>>
>> The probabilities for y = (T mod 7) + 1 are as follows:
>>
>> P(y=1) = .1430656
>> P(y=2) = .1430016
>> P(y=3) = .1428224
>> P(y=4) = .1426432
>> P(y=5) = .1426432
>> P(y=6) = .1428224
>> P(y=7) = .1430016
>>
>> The above probabilities are exact, hence you can see a slight bias. Of
>> course, while I had originally intuited a bias, I expected it to be
>> badly biased. I was wrong about that. Only the continuous case is
>>
>> quasi

>
>As to the bias, I had pointed it out quite a while ago. Any random
>variable which is a function of a fixed number n of independent
>random variables, each say uniformly distributed on the integers from
>1 to 5, CANNOT be uniformly distributed on the integers from 1 to 7,
>for the very simple reason that 7 does not divide 5^n.

Right, I see that.

Actually, I just posted a problem relating to this issue (I had not

quasi

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
12/24/07 quasi
12/24/07 b92057@yahoo.com