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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 22, 2007 2:04 PM

On Sat, 22 Dec 2007 14:00:57 -0500, quasi <quasi@null.set> wrote:

>On Sat, 22 Dec 2007 13:51:57 -0500, quasi <quasi@null.set> wrote:
>

>>On Sat, 22 Dec 2007 10:43:27 -0800 (PST), vr <simple.popeye@gmail.com>
>>wrote:
>>

>>>On Dec 22, 11:35 pm, quasi <qu...@null.set> wrote:
>>>> On Sat, 22 Dec 2007 10:32:37 -0800 (PST), vr <simple.pop...@gmail.com>
>>>> wrote:
>>>>
>>>>
>>>>
>>>>
>>>>

>>>> >On Dec 22, 11:16 pm, 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- Hide quoted text -
>>>>
>>>> >> - Show quoted text -
>>>>
>>>> >Hmm. Let me simplify it:
>>>>
>>>> >RN_7 = T*3/14 - 0.5
>>>>
>>>> >If you look at T*3/14, it just scales the sum of random numbers
>>>> >uniformly using a constant multiplier. Did I miss to notice any non-
>>>> >uniformity here?

>>>>
>>>> Yes, T is not uniformly distributed in its range.

>>>
>>>Ok. But if S_n is guaranted to be uniformly distributed in the range 1
>>>to 5, then doesn't it mean the sum of 7 such numbers will also get
>>>distributed over 7 to 35? I'm just curious. Thanks.

>>
>>Yes, but not uniformly.
>>
>>What's the chance of getting exactly 35?
>>
>>If it was a uniform distribution it would be 1/29, right?

>
>Of course, that's assuming S is a uniformly distributed integer
>variable on {1,2,3,4,5}.
>
>If instead, S is a uniformly distributed continuous variable on (1,5)
>then we can ask -- what's that chance of getting a result more than
>34? It should be at least 1/28, right?

I meant: It should be (exactly) 1/28, right?

>But it's easily seen to be a lot less than that (the probability is
>bounded above by 1/2^(14)).

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