Let y space S = == (t20) denote a time-homogeneous, continuous-time Markov chain with state {1,2,3} and the generator matrix -2 a 2a G = 1 -4 3 1 2 -3 (a) Determine the value of a. (b) Determine the holding time parameters of y. (c) Calculate the mean holding time of y in state 2. = (d) Let X (Xn ne No) denote the embedded Markov chain of y with P(X₁ =iX0= i)=0, ie S. Calculate the transition matrix of X. [2 marks] [2 marks] [2 marks] [4 marks]