MATH 632 Midterm: 2007 Math 632 - Seppalainen - Spring Exam 1
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Instructions: show calculations and give concise justi cations for full credit. In-class part: consider the markov chain on the state space s = {1, 2, 3, 4} with transition matrix. P3[ there exists a nite number n0 such that xn = 4 for all n n0 ]. (c) (20 pts) find the limits lim p(n) Explain what theorem you are using and what markov chain are you applying it to. n n (d) (15 pts) assuming that the limit lim p(n) 3,1 exists, nd its value. (we do not have a theorem that guarantees its existence, hence the assumption. ) For bonus points, can you give an argument for the existence of this limit? n . Rules for take-home part: no consultation with anyone per- mitted. Not with fellow students, not with internet chat groups, nobody. The take-home part is due by 12 noon tomorrow in the instructor"s o ce: alice and betty shoot baskets.
