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Section 4 Problems

# Section 4 Problems - ORIE3510 Introduction to Engineering...

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ORIE3510 Introduction to Engineering Stochastic Processes Spring 2010 Section 4 problems Problem 1: Ross, 4.67 Problem 2: Zeke prevents bankruptcy Without beneﬁt of dirty tricks, Harry’s restaurant business ﬂuctuates in successive years between three states: 0 (bankruptcy), 1 (verge of bankruptcy) and 2 (solvency). The transition probability matrix is P = 1 0 0 . 5 . 25 . 25 . 5 . 25 . 25 . (a) What is the expected number of years until Harry’s restaurant goes bankrupt assuming he starts in the state of solvency. (b) Harry’s rich uncle Zeke decides it is bad for the family name Harry is allowed to go bankrupt. Thus, when state 0 is entered, Zeke infuses Harry’s business with cash returning him to solvency with probability 1. Thus, the new TPM is P 0 = 0 0 1 . 5 . 25 . 25 . 5 . 25 . 25 . Is this new Markov chain irreducible? Is it aperiodic? What is the expected number of years between cash infusions from Zeke? Problem 3: Harry visits the dentist

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Section 4 Problems - ORIE3510 Introduction to Engineering...

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