bonanova Posted November 19, 2015 Report Share Posted November 19, 2015 You have a coin which is known to be fair: p(H) = p(T) = 0.5 exactly.Devise a method for simulating a biased coin where p(H) = 1/π exactly.Edit:A gold star awaits a method that requires on average only two flips of the fair coin to produce an arbitrary bias. Quote Link to comment Share on other sites More sharing options...
1 CaptainEd Posted November 20, 2015 Report Share Posted November 20, 2015 Aiming at gold star...To smulate a Head with probability P.Write the desired Probability in binary to n digitsFlip the coin. if it matches the ith digit (H=1, T=0), flip again.If it doesn't, announce the opposite of the result. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted November 20, 2015 Author Report Share Posted November 20, 2015 Bingo.Can you determine the expected number of flips needed for p(H) = 1/π ? Quote Link to comment Share on other sites More sharing options...
1 CaptainEd Posted November 20, 2015 Report Share Posted November 20, 2015 I feel like such a buffoon! (I could sum this series in high school, but not now...Please nobody needle me :-( )Expected number of flips in one evaluation1/2 of the evaluations stop with 1 flip1/4 of the evaluations stop with 2 flips1/8 of the evaluations stop with 3 flipsetc.Sum of i/(2^i) is 2 Quote Link to comment Share on other sites More sharing options...
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bonanova
You have a coin which is known to be fair: p(H) = p(T) = 0.5 exactly.
Devise a method for simulating a biased coin where p(H) = 1/π exactly.
Edit:
A gold star awaits a method that requires on average only two flips of the fair coin to produce an arbitrary bias.
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