ping Jim Wells
From: |-|erc (gotch_at_beauty.com)
Date: 07/10/04
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Date: Sat, 10 Jul 2004 07:50:25 GMT
Can you expand on what you meant here. If you toss a fair coin infinite times
will it diverge to one side *either* heads or tails as being the most common,
or does it alternate back and forth with Head and Tails taking turns being in the lead?
Herc
>
> From: Jim Wells (jim@127.0.0.1)
> Subject: Re: estimating probability
> View this article only
> Newsgroups: sci.logic
> Date: 2003-05-04 22:24:50 PST
>
>
> I never mentioned any final result, as an infinte series of tosses would
> have no final toss. That's where you get into trouble trying to utilize
> common statistical techniques; they are designed for use on finite
> sample sets. If the probability of something happenning in one trial is
> P, what are the odds that it will occur once in T trials? The formula is
> 1 - [1 - P] ^ T. Note that as the number of trials becomes infinite, the
> odds of the event happening converge to 1 for all P > 0. Now note that
> in an infinite series of coin tosses, there are an infinite number of
> smaller infinite series of coin tosses, each treatable as a trial for
> the probability that an infinte series of tosses will have an unequal
> number of heads and tails flips. So the two requirements are met, a P >
> 0 and an infinite T. Hence the probability equalling 1 that at least one
> inifinte subset of an inifite series of tosses will manifest a
> disequilibrium one way or the other.
>
>
> From: Jim Wells (jim@127.0.0.1)
> Subject: Re: estimating probability
> View this article only
> Newsgroups: sci.logic
> Date: 2003-05-05 17:35:48 PST
>
>
> Yes, the number of ties will be infinite. There will also be inifinite
> (both in length and in number) periods favoring heads and infinite
> periods favoring tails between the ties. Why? In a random walk, the
> expected wait time for return to origin is infinite. Don't take my word
> for it. See http://www.ms.uky.edu/~mai/java/stat/brmo.html What is the
> expected wait time to go from tied to disequilibrium? Always one toss.
> So even though the coin is fair and will balance out given infinite
> tosses, most of the time there heads will still be unequal to tails.
>
>
-- Free online chess lessons www.chessit.net
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