5. (15 points) Suppose that when you join Checkout Line 1 at Publix, there are three people ahead of you in line. Assume, for simplicity, that the amount of time it takes the cashier to serve each period is exponentially distributed with mean 5 minutes, independently of everything else. (a) Find the expected value of the amount of time it takes to begin receiving service from the cashier. (b) Find the probability that, after having waited for 15 minutes, there is only one person in front of you in line receiving service. (0) Suppose that, if Checkout Line 2 opens and someone is still in front of you at Checkout Line 1 at this instant, you move to Checkout Line 2. Assume that the distribution of the amount of time between When you arrive to Checkout Line 1, and when Checkout Line 2 opens is exponentially distributed with mean 15 minutes, independently of everything else. Find the probability you move from Line 1 to Line 2 before leaving the store