Problem 2. You have two coins in your pocket. One is a standard fair coin, so that P(heads)=0.50. The other one is a two

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Problem 2 You Have Two Coins In Your Pocket One Is A Standard Fair Coin So That P Heads 0 50 The Other One Is A Two 1 (105.56 KiB) Viewed 116 times

Problem 2. You have two coins in your pocket. One is a standard fair coin, so that P(heads)=0.50. The other one is a two-sided coin, so that P(heads)=1. You draw one of the two coins at random and toss it twice. The result is "heads” and “heads”. (a) Use Bayes' formula to obtain the probability that you have selected the two-sided coin, given your observations. 1pt (b) How many consecutive “heads” do you need to observe to be at least 90% certain that the coin is two-sided? lpt (c) Consider a classical approach to testing the null hypothesis: the coin is fair. Let the number of “heads” observed after two tosses be the test statistic. What is the associated p-value. (Hint: look up the definition of the classical p-value.) 1pt