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

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quasi

Posts: 12,057
Registered: 7/15/05
Re: Random numbers
Posted: Dec 22, 2007 2:00 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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? 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
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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