RANDOM COIN TOSSING

A sequence of heads and tails is produced by repeatedly selecting a co in 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 s econd coin is known either to be fair, or to have known bins theta is an element of(0,1] (Prob(heads) -1/2 (1+theta)) Letting u(k):=Prob (Th ere is a renewal at time k), we show that if Sigma(k=0)(infinity)u(k)( 2)=infinity, we can determine, using only the sequence of heads and ta ils produced, if the second coin had bias theta or 0. If Sigma(k=0)(in finity) u(k)(2) <1+1/theta(2), we show that this is not possible.