Consider the critical illness model with 3 States: State 1 is healthy (H), State 2 is critically ill (C), and State 3 is dead (D). Suppose you have a homogeneous Markov Chain with transition probability matrix
P = [0.92 0.05 0.03; 0.00 0.76 0.24; 0.00 0.00 1.00]
(a) Find Q = (I - S)^{-1} for this transition matrix and interpret the entry q_{21}.
(b) If we are currently in State 2, what is the expected number of steps in the process before the absorbing stated is reached?