with state space S = 4. Consider the Markov chain (Xn, n transition matrix

/1/3 1/3 1/3 0 0 0 0
0 1/2 1/2 0 0 0 0 1/4
3/4 1/4 0 1/8 1/2 1/8

(a) Draw the transition diagram for this Markov chain. (b) Find P (X₁ = 2, X2 = 2, X3 = 3, X₁ = 2 | Xo = 1). (c) Find P (X3 = 1 | Xo = 1, X₁ = 3, X₂ = 1). (3) (d) Find p = P(X3 = 3 | Xo = 4). {1, 2, 3, 4, 5, 6, 7}