Consider the continuous time Markov chain {Y (t) : t 2 0} living in the state space {1, 2, 3, 4} with generator matrix -2 NO O O 1 -2 G = 1 -2 OO 2 -2 Define T = min {t 2 0 : Y (t) e {1} } and set u (i) = E; [Tly (0) = i]. Find a system of linear equations satisfied by u (i) for i = 2, 3, 4. Use Monte Carlo to provide a 95% confidence interval for u (2)