Question 6 (7 marks, C5) Alan is a barber. He works from 10:00 A.M. to 5:00 P.M. Suppose that the number of people served by Alan is Poisson random variable with a mean of 3 people per hour. Bill is Alan's supervisor. He visits Alan daily, at a time uniformly distributed between 12:00 P.M. to 5:00 P.M. If X is the number of customers that Alan has served that day when Bill arrives, find the mean and variance of X. Explain your solutions.