MATH 632 Midterm: 2002 Math 632 - Fall Exam 2
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Instructions: hand in problem 1 for 50 points, problem 2 for 30 points, and one other problem for 20 points. Show calculations and justify non- obvious statements for full credit: fix a constant (0, 1), and consider again the markov chain on the state space s = {1, 2, 3, 4, 5, 6} with transition matrix. 0 0 1 0 0. In exam 1 we found the invariant distribution. , 0 , 0 (cid:21) . (a) state the hypotheses under which we proved the convergence theorem pn(1, 3) and explain brie y how pn(x, y) (y) for markov chains. Find lim the hypotheses of the theorem are met. n (b) find the limiting probability lim n . Find the limit of pn(1, 3) as n : customers arrive as a homogeneous poisson process with rate per hour. One customer out of 5 is a member of the store club. The amount a member spends has mean 10 and variance 20.
