Suppose that the probability that it will rain on any given day is 0.230, and that the probability is independent from day to day. Assume that Mary is trying to make a decision on whether to accept her friend's invitation to go to the movies tomorrow. Turning down the invitation means that she will go to play basketball if it is sunny tomorrow and that she can only stay at home if it rains tomorrow. There is a weather forecast that signals whether it will rain tomorrow or not. There is a 0.20 probability of receiving a \"rainy\" forecast. There is a 0.95 probability of a rainy day tomorrow when there is a "rainy" forecast and a 0.05 probability that it will rain when there is a \"sunny" forecast. Assume that Mary is risk neutral. Assume that Mary places different monetary values on the potential outcomes: a sunny day at the basketball court ($90 ), a rainy day at the movies ($20), a rainy day at home (SB25), and a sunny day at the movies ($0). a. If Mary has no weather forecast, what is the expected value of rejecting the invitation to the movies? b. If Mary has no weather forecast, what is the expected value of accepting the invitation to the movies? c. What is the value of perfect information about tomorrow's weather? d. If Mary receives a "rainy" forecast, what is the expected value of accepting the invitation to the movies? e. If Mary receives a "sunny" forecast, what is the expected value of rejecting the invitation to the movies? f. Assume that Mary would choose the optimal decision no matter whether she receives a "rainy" forecast or a "sunny" forecast. What is Mary's expected value prior to receiving the forecast signal