Unformatted text preview: the number of items has fallen under the value s . Immediate demand which cannot be satis±ed from the existing stock, will be satis±ed immediately after restocking. Model the number of items in the stock as a Markov chain. Discuss the properties of irreducibility and aperiodicity. Problem 4: A Markov chain ( X n ) n ≥ with states 0, 1 and 2, has the transition matrix 1 2 1 3 1 6 1 3 2 3 1 2 1 2 If P ( X = 0) = P ( X = 1) = 1 4 , compute E [ X 3 ]. Problem 5: Consider the matrices in Exercise 14 on page 265. 1. Show that they are transition matrices of Markov chains. Determine the state spaces of these Markov chains. 2. Determine the classes of these Markov chains. 3. Which states are recurrent and which are transient? 4. Which of the 4 Markov chains are recurrent and which are transient?...
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 Spring '08
 DENKER
 Stochastic Modeling, Markov chain

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