Re: A simple but confusing question

From: Aleks Jakulin (a_jakulin_at_@hotmail.com)
Date: 10/08/04 

Date: Fri, 8 Oct 2004 19:19:23 +0200

Ian Jermyn wrote:
> 1) Tossing a coin with a delta function prior at 0.5 for its
> probability of coming up white, means that the probability
> of w_{n + 1} given W_{n} is always 1/2.

There is an excellent paper by Persi Diaconis, Susan Holmes and
Richard Montgomery (2004): Dynamical Bias in the Coin Toss

http://www-stat.stanford.edu/~susan/papers/headswithJ.pdf

Abstract:
We analyze the natural process of flipping a coin which is caught in
the hand. We prove that vigorously-flipped coins are biased to come up
the same way they started. The amount of bias depends on a single
parameter, the angle between the normal to the coin and the angular
momentum vector. Measurements of this parameter based on high-speed
photography are reported. For natural flips, the chance of coming up
as started is about .51.

I hope that this will help resolve the present dilemma :)

Best regards,
            Aleks 

-- 
mag. Aleks Jakulin
http://www.ailab.si/aleks/
Artificial Intelligence Laboratory,
Faculty of Computer and Information Science,
University of Ljubljana, Slovenia.

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