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
