Consider a small 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. Suppose the X and Y are independent and have the following probability distributions:
X = # of cars Y = # of buses
Compute the mean, variance and standard deviation of the number of cars on the ferry.
Compute the mean and variance of the number of buses on the ferry.
Compute the mean and variance of total number of vehicles on the ferry.
Compute the mean and variance of the total amount of money collected on the ferry.
Which type of vehicle is bringing in more money?
How much more should we expect from that vehicle per trip?
What is the variance of this amount?
If 10 ferry rides were randomly selected, what's the probability that exactly 3 out of 10 ferries will have exactly 2 cars?
If ferry rides are randomly selected, what's the probability that it will take 4 selections to find the first ferry with two busses?