Question Three (8 marks each - 16 marks) Gerald Black of BlackFly Airline has an exclusive contract to run flights of a four-passenger aircraft to a remote mining center. His contract requires him to fly if there are any passengers wanting to make the trip. His fixed costs per day are $400.00, his fixed costs per flight are $1,200.00, the variable cost per passenger is $25.00, and he charges $850.00 per passenger. He has tracked the number of passengers who flew with him over the past sixty days. His findings are summarized in the following table: Number of Passengers 0 2 3 4 Number of Days 5 12 15 21 7 Of course, he does not fly on days with zero passengers. Assume that this sample gives a good approximation to his future demand patterns. Let G be the random variable: profit on a future day. a) Calculate the Expected Value, E[ G ], Variance, o?[ G ] and standard deviation, of G ], of his future daily profit. [Hint: You can calculate a profit corresponding to each number of passengers. The probabilities of those profits are then determined by the probabilities of the numbers of passengers.] b) Comment briefly on the profitability and volatility of Gerald's business