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Solutions to InClass Homework Problems 1, 2, 3.
1. Problem 30 in chapter 4.
Letting
X
n
be 0 if the
n
th vehicle is a car and letting it be 1 if the vehicle is
a truck gives rise to a twostate Markov chain with transition probability matrix
∙
4
/
51
/
5
3
/
41
/
4
¸
.
The limiting probabilities are the solution of
π
0
=4
/
5
π
0
+3
/
4
π
1
π
1
=1
/
5
π
1
+1
/
4
π
1
π
0
+
π
1
.
Solving these yields
π
0
=15
/
19
,
π
2
/
19
.
That is, 4 out of every 19 vehicles are trucks.
2. Consider the gambler’s ruin problem with
p
=0
.
3
,N
=7
, and an initial
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This document was uploaded on 10/18/2011.
 Spring '09

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