An investor is considering how to invest his money. He has two options either a domestic mutual fund that only invests in the Transportation sector or an international aggressive mutual fund that invests in promising startups in the Commercial St Professional Services sector. The payoff {profit} after one year for these investments depends on the state of economy. The investor thinks that there is 0.35 probability that the economy will improve and 0.65 probability that economy will decline. The estimated payoffs are shown in the table below. State of the Economy Economy Declines [0.65) Dom. Fund 2.600 ?U{} Suppose that the investor has decided to hire a professional economic analyst who will provide additional information about the global and domestic economic outlook. Based on the analyst's past record, the investor has estimated 0.7? probability that the analyst would present a favourable report given the economy actually improves, and 0.91 probability that the analyst would present an unfavourable report given the economy actually declines. Economy Improves {0.35) Round all probability values to 4 decimals places. (a) Use this information to fill in the following revised probability table for a favourable report. Probability Revisions given a Favourable Report State of Prior Conditional Probability Joint Posterior Probability Nature Probability P(Fav./State of Nature) Probability P(State of Nature/Fav. Economy Declines Economy Improves P(Favourable) = 1.0000 P(Economic Improvement | Favourable report) = (b) Use this information to fill in the following revised probability table for an unfavourable report. Probability Revisions given an Unfavourable Report State of Prior Conditional Probability Joint Posterior Probability Nature Probability P(Unfav./State of Nature) Probability P(State of Nature/Unfav.) Economy Declines Economy Improves P(Unfavourable) = 1.0000 P(Economic Improvement | Unfavourable report) =