Exercise 1 Using Bayes' decision rule, consider the decision analysis problem having the following payoff table (in units of thousands of dollars): (a) Which alternative should be chosen? What is the resulting expected payoff? (b) It is believed that the prior probability p(S1)=0.2 is just about right, but is uncertain about the splitting of the probabilities for states of nature S2 and S3. Perform a sensitivity analysis on the probabilities for S2 and S3 (without changing the prior probability for S1 ) and comment on the implications of the result of the analysis (c) Suppose that the opportunity is offered to provide information which will tell you with certainty which state of nature will occur. What is the maximum amount you should pay for the information