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Question_from_my_Spring_2008_STAT_333_ex

# Question_from_my_Spring_2008_STAT_333_ex - Question from my...

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Question from my Spring 2008 STAT 333 exam Consider a continuous-time Markov Chain with state space S = {1, 2, 3}. The amount of time spent in state i before jumping is exponentially distributed with rate i , and given that a transition occurs, the instantaneous transition probabilities are given by P ij = 2 2 i j i . a) Find the generator matrix Q for this chain. First of all, we can write out the instantaneous transition matrix P to see what it looks like: ? = 0 1 3 2 3 1 2 0 1 2 2 3 1 3 0 We know the diagonal elements of Q are the negatives of the rates, and the off-diagonals are the rate * Pij. So:
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• Spring '08
• Chisholm
• Markov chain, 20%, continuous-time Markov chain, instantaneous transition, instantaneous transition probabilities, instantaneous transition matrix

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