From: Emlyn O'regan (oregan.emlyn@healthsolve.com.au)
Date: Thu Sep 26 2002 - 20:09:25 MDT
Say there is bias, so that probability of a 1 in any position is, say, 0.55
.
You flip every second bit, so that the probability is now 0.55 of getting a
1 in position i is 0.55 for even values of i, and 0.45 for odd values of i.
For a random value of i, p is 0.5 of getting a 1, assuming that you don't
know there is the odd even rule. But,
1 - it would seem clear that an analysis of a long enough stream of these
bits could uncover the odd/even rule
2 - anywhere you spot a 1, you could guess that the next digit will be a 0,
and visa versa; sequences of 101 will be more common than sequences of 111,
for example.
The problem with bias comes from the highly predictable way in which you try
to correct for it. If instead you were to decide randomly for each position,
to either flip it or not, with equal probability, then you'd be ok. But then
you have no unbiased stream of random numbers to make this decision with,
unfortunately :-)
Emlyn
> -----Original Message-----
> From: gts [mailto:gts_2000@yahoo.com]
> Sent: Thursday, 26 September 2002 13:09
> To: extropians@extropy.org
> Subject: Re: True random numbers wanted
>
>
>
> --- Hartmut <hartmut@ccc-hanau.de> wrote:
> > gts wrote:
>
> > > I don't believe that is true. If a given number in
> > the final unbiased
> > > sequence has equal probability of being 1 or 0 (as
> > is the case) then
> > > each of the two possible outcomes for a given
> > trial has probability 1/2.
> > > It follows that each of the four possible outcomes
> > for two successive
> > > trials has probability 1/4.
>
> > 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
>
>
>
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