7.45. Let Xn be an irreducible recurrent Markov chain of period d≥ 2. Let P be its transition probability matrix and Pd its d-step transition matrix. Show that the state space is a union of d disjoint sets Eo,... Ed-1 such that (a) Each E is an equivalence class for Pd. (b) If Xo Є Eo, then X₁ = E₁, X2 Є E3,...,Xd-1 € Ed-1 and Xd Є Eo.