Consider a large ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let x and y denote the number of cars and buses, respectively, carried on a single trip. Cars and buses are accommodated on different levels of the ferry, so the number of buses accommodated on any trip is independent of the number of cars on the trip. Suppose that x and y have the probability distributions shown below. 1 3 4 5 p(x) 0.07 0.1 0.23 0.29 0.21 0.1 y 1 2 P(y) 0.45 0.35 0.20 It can be easily verified that u = 2.77, o, = 1.3480, u, = 0.75, and o, = 0.7665. (a) Calculate the mean of z = total number of vehicles (cars and buses) on the ferry. Calculate the variance of z = total number of vehicles (cars and buses) on the ferry. (Round your answer to two decimal places.) (b) Calculate the mean (in dollars) of w = total amount of money collected in tolls. 2$ Calculate the variance of w = total amount of money collected in tolls. (Round your answer to two decimal places.)

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