Let {Xn} be a homogeneous Markov chain. (a) Prove that P.' > (Pi,i)2. (b) Provide an example of a chain (specifying the transition matrix is sufficient, please keep it as simple as possible) for which P() 1,1 = (P1,1) 2. (c) Provide an example of a chain (specifying the transition matrix is sufficient, please keep it as simple as possible) for which P(2) 1,1 > (P1,1) 2