Stochastic

# 2 wins 78 34 23 23 verify the results in the table you

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Unformatted text preview: te a four-state Markov chain with states 1, 2, 3, and 4 where 3 = a part that was scrapped and 4 = a part that was sold for a proﬁt. (b) Compute the probability a part is scrapped in the production process. 1.56. A bank classiﬁes loans as paid in full (F), in good standing (G), in arrears (A), or as a bad debt (B). Loans move between the categories according to the following transition probability: F G A B F 1 .1 .1 0 G 0 .8 .4 0 AB 00 .1 0 .4 .1 01 What fraction of loans in good standing are eventually paid in full? What is the answr for those in arrears? 1.57. A warehouse has a capacity to hold four items. If the warehouse is neither full nor empty, the number of items in the warehouse changes whenever a new item is produced or an item is sold. Suppose that (no matter when we look) the probability that the next event is “a new item is produced” is 2/3 and that the new event is a “sale” is 1/3. If there is currently one item in the warehouse, what is the probability that the warehouse will become full before it becomes empty. 1.58. Six children (Dick...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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