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Random coin tossing

Summary.

A sequence of heads and tails is produced by repeatedly selecting a coin from two possible coins, and tossing it. The second coin is tossed at renewal times in a renewal process, and the first coin is tossed at all other times. The first coin is fair (Prob(heads)=1/2), and the second coin is known either to be fair, or to have known biasθ∈(0,1] (Prob(heads) ). Letting u k := Prob (There is a renewal at time k), we show that if ∑ k =0 u k 2=∞, we can determine, using only the sequence of heads and tails produced, if the second coin had bias θ or 0. If , we show that this is not possible.

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Received: 20 November 1996 / In revised form: 20 February 1997

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Harris, M., Keane, M. Random coin tossing. Probab Theory Relat Fields 109, 27–37 (1997). https://doi.org/10.1007/s004400050123

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  • Mathematics Subject Classification (1991): 60K35
  • 60G30
  • 60G42