# Question

Let be the sum of independent rolls of a fair (cubicle) die.

(a) Is X [n] a Markov chain?

(b) Define a new process according to Y[n] = X[n] mod 3. That is, Y[n] Ɛ{ 0, 1, 2} is related to X [n] X [n] = 3q+ Y[n] for a non- negative integer q. Find the transition probability matrix for the process Y [n].

(c) Now suppose Z [n] = X [n] mod 5. Find the transition matrix for Z [n].

(a) Is X [n] a Markov chain?

(b) Define a new process according to Y[n] = X[n] mod 3. That is, Y[n] Ɛ{ 0, 1, 2} is related to X [n] X [n] = 3q+ Y[n] for a non- negative integer q. Find the transition probability matrix for the process Y [n].

(c) Now suppose Z [n] = X [n] mod 5. Find the transition matrix for Z [n].

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