Simulation Problem #5 (20 points) - Crowded Arrivals of Customers a.) (10 points) Assume that the interarrival times An, Arg, Arg, ..., Art\" for :1 customers into a post ofce are exponential with parameter A, so that Ark ~ Expl) for k - 1,2, 3, . .. ,n. Compute the theoretical probability that no two customers arrive within a time 6 > 0 of each other. Your nal answer should involve only a, A and 0. Note that this is one way to address the crowed arrivals of customers. b.) (10 points) Using Excel, or any other program, run a simulation of consisting 1000 runs using n - 10 customers, 1M - 5 minutes and 6 - 0.8 minutes and compare the simulated result to your theoretical calculation in part (a). Note that to simulate an exponential random variable X having parameter A. from a random number R ~ U[0, 1) you may use the equation X - % 1n(R) which we shall derive in Chapter 8