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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 24, 2007 12:32 AM
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On Mon, 24 Dec 2007 00:10:57 -0500, quasi <quasi@null.set> wrote:

>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


Hehe -- I take back part of my apology. It _is_ biased, but only
slightly.

The probabilities for y = (T mod 7) + 1 are as follows:

P(y=1) = .1430656
P(y=2) = .1430016
P(y=3) = .1428224
P(y=4) = .1426432
P(y=5) = .1426432
P(y=6) = .1428224
P(y=7) = .1430016

The above probabilities are exact, hence you can see a slight bias. Of
course, while I had originally intuited a bias, I expected it to be
badly biased. I was wrong about that. Only the continuous case is
badly biased.

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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