A wealthy investor has been offered three major investments, and he likes to choose one. The first, a conservative investment, would do well in an improving economy or would suffer a small loss in a worsening economy. The second, a speculative investment, would do very in an improving economy or very bad in a worsening economy. The third, a counter-cyclical investment, would do bad in an improving economy or very well in a worsening economy. The investor believes there are three possible scenarios over the lives of these potential investments: 1) an improving economy, 2) a stable economy, and 3) a worsening economy. His prior probabilities are 0.1, 0.5, and 0.4 respectively. Profit estimation: for conservative investment is 30 million for scenario 1, 5 million for 2, and -10 for million for 3; for speculative investment is 40 million for scenario 1, 10 million for 2, and -30 million for 3; and for counter-cyclical investment is -10 million for scenario 1, 0 for 2, and 15 million for 3. What should be the investor choice according to: 1) maximum payoff criterion? 2)maximum likelihood criterion? 3) Baye's decision rule?