Let {Xn,n 2 1} be i.i.d. with P(X1) = p = 1– P(X1 = 0). What is the probability that the pattern 1, 0, 1 appears infinitely often? %3D Hint: Let Ak = [Xk = 1, X+1 = 0, X+2 = 1]

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Chapter1: Combinatorial Analysis
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7. Let {Xn, n > 1} be i.i.d. with P(X1) = p = 1- P(X1 = 0). What is the
probability that the pattern 1, 0, 1 appears infinitely often?
Hint: Let
Ak = [Xk = 1, Xk+1 = 0, Xk+2 = 1]
and considers A1, A4, A7,.
Transcribed Image Text:7. Let {Xn, n > 1} be i.i.d. with P(X1) = p = 1- P(X1 = 0). What is the probability that the pattern 1, 0, 1 appears infinitely often? Hint: Let Ak = [Xk = 1, Xk+1 = 0, Xk+2 = 1] and considers A1, A4, A7,.
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