Inscrit le: 20 Juin 2017
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|Posté le: Mer 27 Sep - 07:35 (2017) Sujet du message: Determining that a coin is fair
|I feel as though I must be thinking about this problem incorrectly because I don't think it should be as hard as I'm making it.
Suppose you have a coin such that the probability of getting heads is an unknown value p. How many times should it be tossed to determine that p is within some fixed epsilon of being fair with some specified degree of confidence?
Given a set of coin tosses, it is easy to decide whether the coin is fair with various levels of confidence, but this problem is to determine the number of coin tosses *in advance* based on the desired level of confidence and accuracy. Of course at the end of that run, there will be some set of parameters that can be used to draw a conclusion.
So to put specific numbers on the problem, let's say I have a coin and I want to determine whether 0.49 < P(heads) < 0.51 with 95% confidence when spun. How many times should I plan to spin the coin and what are the conditions that need to be met?
My gut is telling me that there's something about this problem that's ill-posed, but I can't articulate exactly what it is.
I didn't find the right solution from the Internet.