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Pstat160A
Winter 2009
Quiz discussion #1
Wednesday, March 11
Problem 1:
Short questions.
1) Give an application of the reﬂection principle (just state, no explanations)
We found the distribution of the maximum and the number of paths that hit (or doesn’t hit) the
x

axis.
2) Can a Markov chain go from a transient class to another transient class?
Yes. There are no particular reasons to rule this out.
Problem 2:
Consider the Markov chain with transition matrix
P
below.
1. Give the classes, their properties (transience, recurrence) and the period.
P
=
.
4
.
6
0
0
0
.
4
.
6
0
0
0
0
.
6
0
.
4
0
0
0
.
4
0
.
6
0
0
0
1
0
classes:
{
1
,
2
}
,
{
3
,
4
,
5
}
property:
R,
T
period:
1
,
2
2. Use the matrices given at the bottom of the page (and
P
above, to which they relate) to answer the questions
below. Also recall the following formulas:
f
ij
=
s
ij
s
jj
, i
6
=
j
;
f
jj
=
s
jj

1
s
jj
a) What is the column of 1.6667 represent in the ﬁrst matrix below
It represents the expected number of steps in 3, starting (respectively) from 3, 4 or 5
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 Spring '08
 EduardoMontoya

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