Barber shop. There are 2 waiting chairs and 2 barbers. Customers arriving to fully occupied shop are turned away. Assume customers arrive with Poisson rate S/hour and service rate is exponential with rate 2/hour. Let X(t) = #customers in the shop E {0, 1,2,3,4). In other words, the transition rates diagram is as follows 5 5 5 5 1 2 3 0 A 2 (i) Find P(X(() = 4| X(0) =2) 1 = 1,2, 4,8 hours (numerical approximation) (ii) Find the stationary distribution