=+8.32. A sequence {X„) is a Markov chain of second order if P[X,+1 =j|Xo =

io ,.... X„ =i ,, ] = P[X]+; = j|X"-1=in-"X]=i,] =p ;_ ; Show that noth-

ing really new is involved because the sequence of pairs (X ,,, X .. +1) is an ordinary Markov chain (of first order). Compare Problem 8.29. Generalize this idea into chains of order r.