45. Consider a system that can be in either state 1 or 2 or 3. Each time the system enters state i it remains there for a random amount of time having mean μi and then makes a transition into state j with probability Pij . Suppose P12 = 1, P21 = P23 = 12, P31 = 1

(a) What proportion of transitions takes the system into state 1?

(b) If μ1 = 1, μ2 = 2, μ3 = 3, then what proportion of time does the system spend in each state?