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3.2.5 A Markov chain has the transition probability matrix 0 1 2 0 0.7 0.2 0.1 P= 1 0.3 0.5 0.2 2 0 0 1 The Markov chain starts at time zero in state Xo = 0. Let T= min{n ≥ 0; Xn=2} be the first time that the process reaches state 2. Eventually, the process will reach and be absorbed into state 2. If in some experiment we observed such a

3.2.5 A Markov chain has the transition probability matrix 0 1 2 0 0.7 0.2 0.1 P= 1 0.3 0.5 0.2 2 0 0 1 The Markov chain starts at time zero in state Xo = 0. Let T= min{n ≥ 0; Xn=2} be the first time that the process reaches state 2. Eventually, the process will reach and be absorbed into state 2. If in some experiment we observed such a

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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3.2.5 A Markov chain has the transition probability matrix 0 1 2 0.2 0.1 0.5 0.2 0 1 0 0.7 P= 1 0.3 2 0 The Markov chain starts at time zero in state Xo = 0. Let T= min{n ≥ 0; Xn = 2} be the first time that the process reaches state 2. Eventually, the process will reach and be absorbed into state 2. If in some experiment we observed such a process and noted that absorption had not yet taken place, we might be interested in the conditional probability that the process is in state 0 (or 1), given that absorption had not yet taken place. Determine Pr{X3 = 0|X0, T > 3}. Hint: The event {T > 3} is exactly the same as the event {X3 ‡ 2} = {X3 = 0} U {X3 = 1}.
Transcribed Image Text:3.2.5 A Markov chain has the transition probability matrix 0 1 2 0.2 0.1 0.5 0.2 0 1 0 0.7 P= 1 0.3 2 0 The Markov chain starts at time zero in state Xo = 0. Let T= min{n ≥ 0; Xn = 2} be the first time that the process reaches state 2. Eventually, the process will reach and be absorbed into state 2. If in some experiment we observed such a process and noted that absorption had not yet taken place, we might be interested in the conditional probability that the process is in state 0 (or 1), given that absorption had not yet taken place. Determine Pr{X3 = 0|X0, T > 3}. Hint: The event {T > 3} is exactly the same as the event {X3 ‡ 2} = {X3 = 0} U {X3 = 1}.
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