A small town beauty salon has two stylists, Angel and Barbara, and an additional chair for one waiting customer

A small town beauty salon has two stylists, Angel and Barbara, and an additional chair for one waiting customer. If a customer arrives when there are three customers in the salon, she leaves. From the past experience, the average time between arrivals of customers is 30 minutes. Angel completes serving a customer at a rate of 30 minutes, while Barbara does it in an hour. Angel has priority serving the customer since she is faster than Barbara, when there is only one customer in the shop. Further assume that inter-arrival times and service times of customers are independent exponential random variables.   (a)Draw a state transition diagram with possible states and corresponding birth/death rates.   (b)After a long time pass, what is the probability that the shop is empty?    (c)What is the pmf of the number of customers in the shop?    (d)After a long time pass, what is the probability that an arriving customer is turned away?     (e)What is the distribution of the number of customers arriving in the first 3 hours?   (f)What is the probability that no customer arrives in a 3-hour time interval?      (g)What is the mean number of arrivals in 3 hours?     (h)What is the distribution of the time until the fifth customer arrives?  (i)What is the probability that the time until the fifth customer arrives is <2.5>