7.33 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 following probability distributions:

x 0 1 2 3 4 5 p(x) .05 .10 .25 .30 .20 .10 y 0 1 2 p(y) .50 .30 .20

a. Compute the mean and standard deviation of x.

b. Compute the mean and standard deviation of y.

c. Compute the mean and variance of the total amount of money collected in tolls from cars.

d. Compute the mean and variance of the total amount of money collected in tolls from buses.

e. Compute the mean and variance of z 5 total number of vehicles (cars and buses) on the ferry.

f. Compute the mean and variance of w 5 total amount of money collected in tolls.