From: Charles Hixson (charleshixsn@earthlink.net)
Date: Thu Sep 26 2002 - 15:37:01 MDT
gts wrote:
>--- Hartmut <hartmut@ccc-hanau.de> wrote:
>
>
> ...
>
>
>
>
>>Sorry, but that is not correct. You can't say, that
>>if 0 and 1 have probability 1/2, the probablity
>>distribution also holds for longer subseries.
>>
>>
>
>I beg to differ. The sequence of 1's and 0's in the
>unbiased sequence will follow a binomial distribution,
>no different from a series of coin-flips.
>
>
>
>>Your method would only work, if 0s and 1s got each
>>50% probability,
>>
>>
>
>And that is case for the final unbiased sequence.
>
>-gts
>
>
>
No sequence of random numbers is unbiased after they have been selected,
no matter how the selection was done. It will not necessarily come out
to a 50-50 distribution, even if that was the initial estimate of
probability made with full knowledge of all deterministic factors.
Theoretically, the 50-50 distribution is accurate only for an infinite
sequence of numbers, but even then if you initially start with some
particular finite subset of those numbers (i.e., ANY particular finite
subset) you don't have a random sequence anymore. Perhaps it is
sufficiently random for your purpose, and perhaps not, but it isn't
truely random.
The best you can do is to select a sufficiently random way of generating
numbers, and take whatever number shows up when you ask for it.
(Several approaches that appeared to approach true randomness
sufficiently for all purpose I can think of were mentioned during the
first day or two of this discussion.)
-- -- Charles Hixson Gnu software that is free, The best is yet to be.
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