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?

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(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.

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(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?