Suppose Alice is sitting at a circular table with 4 chairs labeled {1, 2, 3, 4} and sitting initially at a random chair. Every minute she moves to her left or right at random with equal probability. Consider the Markov chain associated to the sequence of her positions X0, X1, . . .. Write the state space, the distribution of X0 and the distribution of X1. Write the transition matrix. Assume she is at chair one at time t = 0. Write an expression (in terms of numbers PT\"- do not evaluate) for the probability that she will be at 1 again at t = 4 and at a 137 different chair at t = 12