Problem 4.1. Consider a CTMC {X1} on S = {1, 2, 3} with generator matrix 3 2 1 Q: 1 2 1 , 2 1 3 and denote the transition function of {Xi} by {P(t),t 2 0}. (a) Let {M} be a Poisson process with rate A m 3. Find the smallest value M E No such that IP'(N2 > M) g 0.01. (b) Using Poisson subordination and part (a), nd an estimate 13(2) such that A max |P(2) _ my <_: without explicitly computing the transition flmltion of compute limiting distri bution if chain starts at x0="1," in long term what proportion time will it spend state>