MATH 632 Midterm: 2002 Math 632 - Fall Exam 1
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1 for 60 points, and one other prob- lem for 40 points. Show calculations and justify non-obvious statements for full credit. 0 0 1 0 0. 0 (a) draw the arrow diagram for the markov chain. Classify the states according to recurrence and transience. Find the periods of recurrent states. (be careful here because your subsequent answers depend on this part. ) (b) find the probabilities 2,4 and 6,5, and the expectations e2n (4) and. E2n (6). (c) find the probability p3[x3 = 3, x6 = 3, x9 = 3, . , x3k = 3] for an arbitrary positive integer k. (d) find an invariant distribution . (e) find the probability p [x100 = 4 or x101 = 4]. S = z+ = {0, 1, 2, 3, . and transition probabilities p(x, x + 1) = and p(x, 0) = 1 for all x.
