ISyE 3232
Stochastic Manufacturing and Service Systems
Fall 2011
H. Ayhan
Homework 8
October 24, 2011
(Due: at the start of class on Monday, October 31)
1. Consider two stocks. Stock 1 always sells for $10 or $20. If stock 1 is selling for $10 today, there is a
.80 chance that it will sell for $10 for tomorrow. If it is selling for $20 today, there is a .90 chance that
it will sell for $20 tomorrow.
Stock 2 always sells for $10 or $25. If stock 2 sells today for $10 there is a .90 chance that it will sell
tomorrow for $10. If it sells today for $25, there is a .85 chance that it will sell tomorrow for $25.
Let
X
n
denote the price of the 1st stock and
Y
n
denote the price of the 2nd stock during the
n
th day.
Assume that
{
X
n
:
n
≥
0
}
and
{
Y
n
:
n
≥
0
}
are discrete time Markov chains.
(a) What is the transition matrix for
{
X
n
:
n
≥
0
}
? Is
{
X
n
:
n
≥
0
}
irreducible?
(b) What is the transition matrix for
{
Y
n
:
n
≥
0
}
? Is
{
Y
n
:
n
≥
0
}
irreducible?
(c) What is the stationary distribution of
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 Fall '07
 Billings
 Markov chain, stationary distribution, Stochastic Manufacturing, H. Ayhan

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