MATH 632 Final: 2002 Math 632 - Fall Final Exam
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Show calculations and justify non-obvious statements for full credit: (a) (15 pts) suppose xn is a discrete-time markov chain with state space s = {1, 2} and transition matrix. 1 (cid:21) where , (0, 1). Start the chain with its invariant distribution . For positive integers m3 > m2 > m1 > 0, calculate the probability. P (cid:8)xn = 1 for m1 n m2, xn = 2 for m2 < n m3 (cid:9). (b) (15 pts) suppose x(t) is a continuous-time markov chain with state space s = {1, 2} and rate matrix. Find the value of the limit lim t . P1(cid:8)there are no jumps during time interval (t, t + r](cid:9): (20 pts) two transportation routes 1 and 2 operate independently of each other between points a and b. The system has 4 parameters, 1, 1, 2, and 2.
