1. Consider a Markov chain with state space S := {-n, -n + 1,... 1, 0, 1, ...,n - 1, n}. States -n and n are absorbing. From state 0, the chain is equally likely to move to -1 or 1. For all other states, the chain moves one node further from 0 with probability p and one node closer with probability q := 1 - p. (a) What is the probability of being absorbed at n starting from state i for all i E S if p = q = 1/2? (b) What is the probability of being absorbed at n starting from state i for all i E S if p #