You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem: Alternative A State of nature si S2 400 - 100 0 100 0.4 0.6 A2 Prior Probability (a) Which alternative should be chosen under the maximum payoff criterion? (10 points) (b) Which alternative should be chosen under the maximum likelihood criterion? (10 points) (c) Which alternative should be chosen under Baye's decision rule? (10 points) (d) Model this decision problem as a decision tree ( 10 points) You have the option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S, the research will accurately predict Si 60 percent of the time (P[Research = Si|State =Si] =0.6), but inaccurately predict S2 40 percent of the time (P[Research = S2|State =Si] = 0.4). When the true state of the nature is S2, the research will accurately predict S2 80 percent of the time, but will inaccurately predict Si 20 percent of the time. (e) Including the decision of whether or not to perform the research, represent this decision problem as a decision tree. Define appropriate chance probabilities and find each branch profit. (10points) (f) It is worthwhile to perform the research? (10points) (g) Determine the optimal policy regarding whether to do the research and the choice of the decision alternative. (10 points) You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem: Alternative A State of nature si S2 400 - 100 0 100 0.4 0.6 A2 Prior Probability (a) Which alternative should be chosen under the maximum payoff criterion? (10 points) (b) Which alternative should be chosen under the maximum likelihood criterion? (10 points) (c) Which alternative should be chosen under Baye's decision rule? (10 points) (d) Model this decision problem as a decision tree ( 10 points) You have the option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S, the research will accurately predict Si 60 percent of the time (P[Research = Si|State =Si] =0.6), but inaccurately predict S2 40 percent of the time (P[Research = S2|State =Si] = 0.4). When the true state of the nature is S2, the research will accurately predict S2 80 percent of the time, but will inaccurately predict Si 20 percent of the time. (e) Including the decision of whether or not to perform the research, represent this decision problem as a decision tree. Define appropriate chance probabilities and find each branch profit. (10points) (f) It is worthwhile to perform the research? (10points) (g) Determine the optimal policy regarding whether to do the research and the choice of the decision alternative. (10 points)