If the coin has no internal state, then the sequence of tosses are necessarily i.i.d. random variables. Subject to the (true!) assumption of the tosses being i.i.d., the *only* information you discern from the sequence of outcomes is the multiset of outcomes -- or equivalently the number of heads and number of tails. (Even for a biased coin, P(HT) = P(TH) = sqrt(P(TT) * P(HH)) and so on.) Best wishes, Adam P. Goucher
Sent: Sunday, March 06, 2016 at 7:42 AM From: "David Makin" <makinmagic@tiscali.co.uk> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] how to test whether a coin is fair
? even with no internal state change we know that say probabilities of 2 tosses giving hh, ht, th and tt *ought* to be equal in the long term.
On 5 Mar 2016, at 15:07, Adam P. Goucher wrote:
Because each time you toss a coin, its internal state changes?
Sent: Friday, March 04, 2016 at 11:06 PM From: "David Makin" <makinmagic@tiscali.co.uk> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] how to test whether a coin is fair
I'd guess that you'd actually have to check the evenness of all sample rates, not just a "1" and a "0" but also "00" vs. "01" vs. "10" vs. "11" and "000" vs."001" etc............... i.e, use the same check as for checking the randomness of a pseudo random generator.
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