Problem 1: A coin (not necessarily fair) will be tossed once, and you have to predict the outcome. If you predict the outcome correctly you win $1000. Otherwise, you lose $5.
(a) What are the states of nature? What is the decision space? Write the utility table.
(b) Suppose that you believe that the probability of heads is 2/3. What is your price for the states of nature? Find the expected gains.
(c) Suppose that you are allowed to toss the coin twice and you ?nd that the ?rst toss results in heads and the second in tails. What are the observables?
(d) Assume the situation in (c). The coin is going to be tossed again and you have to predict the outcome. What is your updated prior?
(e) What are your expected gains, and what is your decision for the situation in (d)?