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Markov Chains

R

Richard_07

Member
I find question 8 from April 2004 Exam (Subject 103) a bit confusing.

"pij =nij / ni , where nij is the number of transitions from state i to state j and
ni+ is the total number of transitions out of state i. "

For example, nw = 2 (2 transitions out of state W) and nwc=1 (1 transition from w to c). So the estimate of pnw should equal 1/2, shouldn't it?
Im using the approach from Chapter 3 question 3.24 in the Notes.

However, the way they calculated probabilities is identical to how we would calculate the estimates of transition rates for Markov Jump Process. And I don't understand why...
 
Richard,

The nw is the number of times that the state is W. This equals 8 - you can think of it as the number of transitions out of W, but you have to count transitions from w to w.

Giles
 
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