Consider a large ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Letxandydenote 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 thatxandyhave the probability distributions shown below:x012345p(x)0.060.100.250.270.210.11y012p(y)0.500.100.40

(a) Compute the mean and standard deviation ofx. (Round the answers to three decimal places.)

Mean ofx

Standard deviation ofx

(b) Compute the mean and standard deviation ofy. (Round the answers to three decimal places.)

Mean ofy

Standard deviation ofy

(c) Compute the mean and variance of the total amount of money collected in tolls from cars. (Round the answers to two decimal places.)

Mean of the total amount of money collected in tolls from cars $

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. (Round the answers to one decimal place.)

Mean of the total amount of money collected in tolls from buses $

Variance of the total amount of money collected in tolls from buses

(e) Compute the mean and variance ofz= total number of vehicles (cars and buses) on the ferry. (Round the answers to two decimal places.)

Mean ofz

Variance ofz

(f) Compute the mean and variance ofw= total amount of money collected in tolls. (Round the answers to one decimal place.)

Mean ofw$

Variance ofw