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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]

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]

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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