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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 12:10 AM

On Sun, 23 Dec 2007 19:46:21 -0800 (PST), bill <b92057@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
on the set {1,2,3,4,5,6,7}. While T is clearly biased in the range 7
to 35, apparently (T mod 7) is _unbiased_ in the range 0 to 6. As to
why it's unbiased, I'm not sure. I'll have to think about it.

>Just in case my notation is incorrect;
>if T = 21, then T mod 7+1 = 1;
>If T = 35, T mod 7 +1 = 1.

Right.

>The following is the typical result of my simulation.
>
>1 1209
>2 1115
>3 1180
>4 1189
>5 1191
>6 1131
>7 1171
>TOT 8186

Looks uniform enough.

I thought it would be badly biased.

Oh well -- at least I was right about the continuous case.

I'm glad you took up the challenge to do a simulation. That's the cool
thing about probability. Very often, a simple experiment is all it
takes to validate a true claim or invalidate a false one (to within a
reasonable doubt).

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