Question 1) (25 points) Suppose you visit a small branch of Bank of Sultanate in South Mawaleh that operates a single server with an exponential service time that has rate 1 transaction every 5 minutes. Arrivals at this small branch are Poisson with rate 1 customer every 10 minutes. (a) (9 points) What is the expected time a customer spends in the system? How about the expected time spent in line? What is the average number of customers in the system? (Remark: Present computations for ONLY the performance metrics that I am asking about. Any unnecessary computation will be penalized as well.) (b) (4 points) What is the probability that you observe at least 4 customers in this system when you arrive at this branch? (c) (6 points) Suppose there are 2 other customers in the system when you arrive. What is the expected time you will spend in the system? Is this the answer same as what you have in part (a)? Why? Explain. (d) (6 points) Suppose there is a maximum capacity of 4 customers in this small branch. Calculate the expected time a customer spends in the system. How does this compare to your answer in part (a)? Why? Explain