Let {Yk | k = 0 1 . . . } denote a sequence of independent and identically

distributed (i.i.d.) discrete random variables. These random variables are governed by

the probability distribution [p1 p2 . . . pi . . . ] where pi = P{Yk = i} for all i = 1 2 . . . .

Define

Xn = [0 for n = 0 Xn = [ summation (k=1 to n) Yk for n = 1 2 . . . .

(a) Show that X = {Xn n = 0 1 2 . . . } is a Markov chain.

(b) Compute the transition probability matrix for X in terms of {pi}.

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