Find the PSD of the process described in Exercise 8.1. For a Markov chain, prove or disprove

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Find the PSD of the process described in Exercise 8.1. For a Markov chain, prove or disprove the following statement:
Pr (Xk = ik | Xk + 1 = ik + 1, Xk + 2 = ik + 2… Xk+ m = ik+ m) = Pr (Xk = ik | Xk + 1 = ik + 1)
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