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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 Spring '09
 RESNIK
 Probability theory, Stochastic process, Harry, Markov chain

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