Tue:- neighbouring houses each have a wi hub. Both hubs have three radio channels available to them, labeled 1, 2, 3. Each huh attempts to update the channel it uses, independently of the other, at the times of a rate 1 Poisson prooms, In order to avoid interference, the channel is chosen with equal probabilities hen: the two possibilities not currently used hp the other hub, The behaviour of the hubs can be modeled by a continuous-time Markov chain on the state space I = {11, 12, 13, e1, 22, 23, 31, 22, 33}. Note that some update attempts do not result in a jump of the Markov chain: for example, if the current state is 12, and the rst coordinate attornpts to update to channel 1, there is no jump. {a} Find the communicating classes, and for each one state 1whether it is transient or recurrent. [3] {b} Assume the chain starts in state 12. Find the expected number of jumps of the Markov chain required to reach state 21. [3]