Consider a continuous-time Markov chain with X(0) = 0. Let A denote a set of states that does not include 0 and set T = Min{t > 0. X(t) = A} Suppose that T is finite with probability 1 Set q, 9.,, and consider the random variable H = , qx(t) dt, called the random hazard.

(a) Find the hazard rate function of H That is, find lim P{s