Suppose that the number of customers arriving at an automobile dealership in Chicago follows a Poisson process with = 3 (time is measured in hours).

1. What is the probability that at most two customers arrive in the first hour?

2. Suppose that exactly two customers arrive in the first hour. What is the probability that there will be exactly three customers in the second hour?

3. Suppose that exactly four customers arrived in the first two hours. What is the prob- ability that exactly two customers arrived in the first hour?

4. An enthusiastic salesperson decides to wait until 10 customers have arrived before going to lunch. What is the expected amount of time she will have to wait?

5. Let N denote the number of customers that arrive in the first two hours. Find E[N2].