MATH 419 Study Guide - Midterm Guide: Medieval Commune, Exclusive Or, Poisson Point Process
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You can use parts of problems to prove other parts without having done the parts. When you want to use a theorem brie y state hypotheses. for example: Figure 1: (10 points) let s = (sn, n = 0, 1, 2, . be a random walk on the state space v whose elements are the vertices in the graph in figure 1. Page 3 of 12 (c) does p(sn = x) converge, as n , to x for each x v ? (d) does 1 m=1 npn. Pj s pijhj (b) suppose t is the last time n 0 such that xn a. Page 5 of 12 (c) suppose that h = (hi, i s) is a non-negative solution to (1). Show that, for i 6 a, hi = pi(hx . Pii1pi1i2hi2. (2) (d) if h 0 solves (1), is hi = ei(cid:0)fx .
