For the situation of Exercise 6b, in the case of the symmetric walk, let T_u be the random time it takes for the process to reach either level 0 or a. Find E{T_u} for a = 4 and u = 0,1,2,3, 4.

Exercise 6b

Show that the random walk process in Section 2.2.4 is a Markov chain. Find the transition matrices for the following two cases.

(b) The process comes to a stop when X_t = 0 or a, as it was assumed in Section 2.2.4. In this case, X_t may assume values 0,1, ...,a.