G consider the random walk on the 5-cycle. That is Ω = {1, 2, 3, 4, 5} and the transition probability matrix is 0 1 0 0 1 22 1 0 1 0 0 2 1 2 1  P =0 0 0. 2121 0 0 2 0 2 12 0 0 21 0 (a) Let τ1 denote the hitting time of the state 1. Let fk = Ek(τ1). Note that f1 = 0. Write down a recursive equation for {fk, k = 1,2,...,5}. (b) Solve the above recursion to get a formula for fk. (c) Now let τ denote the hitting time of {3,4}. Find P1(Xτ = 3) and E1(τ) by using known formulas about simple symmetric random walk on the integers.