1. You are given the opportunity to guess whether a coin is fair or two-headed, where the prior probabilities are 0.5 for each of these possibilities. If you are correct, you win $5; otherwise, you lose $5. You are also given the option of seeing a demonstration flip of the coin before making your guess. You wish to use Bayes’ decision rule to maximize expected profit.
(a) Develop a decision analysis formulation of this problem by identifying the alternative actions, states of nature, and payoff table.
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(b) What is the optimal action, given that you decline the option of seeing a demonstration flip?
(c) Find EVPI.
(d) Use the procedure presented in Sec. 15.3 to calculate the posterior distribution if the demonstration flip is a tail. Do the
same if the flip is a head.
(e) Use the corresponding Excel template to confirm your results in part (d).
(f ) Determine your optimal policy.
(g) Now suppose that you must pay to see the demonstration flip. What is the most that you should be willing to pay?