stat2303_tutorial06

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online