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3. Let (Sn: n ≥ 0} be a simple random walk with So= 0, and show that Xn = |Sn] defines a Markov chain; find the transition probabilities of this chain. Let Mn max (Sk 0 ≤ k ≤ n}, and show that Yn = MnSn defines a Markov chain. What happens if So # 0? =

3. Let (Sn: n ≥ 0} be a simple random walk with So= 0, and show that Xn = |Sn] defines a Markov chain; find the transition probabilities of this chain. Let Mn max (Sk 0 ≤ k ≤ n}, and show that Yn = MnSn defines a Markov chain. What happens if So # 0? =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 12EQ: 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...
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3. Let {Sn : n > 0} be a simple random walk with So = 0, and show that Xn = |Sn| defines a Markov chain; find the transition probabilities of this chain. Let Mn = max{S& : 0 < k < n}, and show that Yn = Mn – Sn defines a Markov chain. What happens if So + 0? %3D
Transcribed Image Text:3. Let {Sn : n > 0} be a simple random walk with So = 0, and show that Xn = |Sn| defines a Markov chain; find the transition probabilities of this chain. Let Mn = max{S& : 0 < k < n}, and show that Yn = Mn – Sn defines a Markov chain. What happens if So + 0? %3D
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