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

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quasi

Posts: 12,054
Registered: 7/15/05
Re: Random numbers
Posted: Dec 22, 2007 8:25 PM
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On Sat, 22 Dec 2007 16:30:20 -0800 (PST), bill <b92057@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.

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


Date Subject Author
12/21/07
Read Random numbers
Champ
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Marshall
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Phil Carmody
12/21/07
Read Re: Random numbers
Marshall
12/21/07
Read Re: Random numbers
briggs@encompasserve.org
12/21/07
Read Re: Random numbers
William Elliot
12/21/07
Read Re: Random numbers
quasi
12/22/07
Read Re: Random numbers
William Elliot
12/21/07
Read Re: Random numbers
Pubkeybreaker
12/21/07
Read Re: Random numbers
b92057@yahoo.com
12/22/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
simple.popeye@gmail.com
12/21/07
Read Re: Random numbers
simple.popeye@gmail.com
12/22/07
Read Re: Random numbers
quasi
12/22/07
Read Re: Random numbers
Gib Bogle
12/22/07
Read Re: Random numbers
quasi
12/21/07
Read Re: Random numbers
Marshall
12/22/07
Read Re: Random numbers
simple.popeye@gmail.com
12/22/07
Read Re: Random numbers
quasi
12/22/07
Read Re: Random numbers
simple.popeye@gmail.com
12/22/07
Read Re: Random numbers
quasi
12/22/07
Read Re: Random numbers
quasi
12/22/07
Read Re: Random numbers
quasi
12/22/07
Read Re: Random numbers
simple.popeye@gmail.com
12/22/07
Read Re: Random numbers
quasi
12/23/07
Read Re: Random numbers
simple.popeye@gmail.com
12/23/07
Read Re: Random numbers
simple.popeye@gmail.com
12/23/07
Read Re: Random numbers
simple.popeye@gmail.com
12/23/07
Read Re: Random numbers
simple.popeye@gmail.com
12/23/07
Read Re: Random numbers
simple.popeye@gmail.com
12/22/07
Read Re: Random numbers
adder
12/22/07
Read Re: Random numbers
simple.popeye@gmail.com
12/22/07
Read Re: Random numbers
Herman Rubin
12/22/07
Read Re: Random numbers
adder
12/22/07
Read Re: Random numbers
b92057@yahoo.com
12/22/07
Read Re: Random numbers
quasi
12/23/07
Read Re: Random numbers
b92057@yahoo.com
12/23/07
Read Re: Random numbers
quasi
12/23/07
Read Re: Random numbers
b92057@yahoo.com
12/24/07
Read Re: Random numbers
quasi
12/24/07
Read Re: Random numbers
quasi
12/24/07
Read Re: Random numbers
adder
12/24/07
Read Re: Random numbers
quasi
12/24/07
Read Re: Random numbers
adder
12/24/07
Read Re: Random numbers
b92057@yahoo.com

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