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 ]
 quasi Posts: 12,067 Registered: 7/15/05
Re: Random numbers
Posted: Dec 22, 2007 8:25 PM

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.

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 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