Suppose we want to know the average (or expected) number of steps it will take to go from state i to state j in a Markov chain. It can be shown that the following computation answers this question: Delete the jth row and the jth column of the transition matrix P to get a new matrix Q. (Keep the rows and columns of Q labeled as they were in P.) The expected number of steps from state i to state j is given by the sum of the entries in the column of (I - Q)-1 labeled i.
In Exercise 11, if the piñon nut crop is fair one year, what is the expected number of years until a good crop occurs?
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