stat2303_tutorial06

# 3 05 02 0 1 20 the markov chan starts at time zero

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Unformatted text preview: e Markov Chan starts at time zero and 0. Let 0| 2 be the first time that the process reaches state 2. Note that the process will eventually be absorbed into state 2. But, if in some experiment we observed such a process with absorption 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 0| 0 ,T 2 Note that 1. 0 2. 2 1, i.e. 2& 1 2& 2 0 2 Since 0| 0 ,T 2 0, 2, 2, 0, 2, 2 0, 2, 2 0, 2, 2 0, 2, 0 0, 2, 2 0, 0, 0 0, 0, / 1, 0, 0| 0| 0, 2 0, 0 0 1, 0, 1, 0 1, 1, 0 0 As 0, 0, 0 0| 0, 1, 0 0| 1, 0, 0 1| 1, 1, 0 1| 0| 0 ,T 0, 1 1 1 1 0 0| 0 0 1, 0 1| 0 0 0, 0 0| 0 0 1, 0 1| 0 0 2 0.7 0.7 0.6962 Alternatively, Because 0| 0.7 0.3 2 1| 2 0.7 0.2 0.1 0.7 0.2 0.3 0.5 0.2 0.3 0.5 0 0 1 0 0 Page 3 of 5 0.7 0.2 0 and 0.1 0.2 1 0.3 0.2 0.2 0.7 0.5 0.55 0.24 0.21 0.36 0.31 0.33 0 0 1 0.2 STAT2303/2803 Probability Modelling/Stochastic Models 0, 0 0, 0| 0| 0| 0, 0, , 0 0 0| 0| 0| , Semester 1, 2010­11 1, 2, 1, 0, 0, 0, 2, 0 0 0 0| 1| 2| 0 0 | 0| 0 0 1| 0 0 0 0 0 0 0, 2, 0 0 0 0 0 1, 0 0 0 Similarly, 2, 0 2, Hence, 0| 0 ,T 2 0| 0, 2, 0, 0 0 0, 0 0| 0 0| 2 0 0, 0 1, 0| 0| 0.55 0.55 0.24 0.6962 Page 4 of 5 0 0 0 0 0 1| 1| 0 0 0 STAT2303/2803 Probability Modelling/Stochastic Models , , … has the transi...
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