Problem 1.2 (10 points) A continuous-time Markov chain with state space S = {1,2,3,4} has nonzero transition rates q(1,2) = q(2, 3) = (1(3, 1) = (1(4, 1) = 1 and q(1,4) = (1(3, 2) = (1(3, 4) = q(4, 3) = 2- (a) Provide (i) the transition rate graph, (ii) the holding time parameters, (iii) the generator matrix, and (iv) the transition matrix for the embedded Markov chain. (b) How long on average will the Markov chain stay in each state before moving to the next state? (c) If the chain is at state 3 and moves next to state 4, how long on average will it stay in state 3 in this case