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Spring 2009 OR3510/5510
Problem Set 2
Due Monday Feb 9 at 10am. You may insert in the homework box between Rhodes and Upson
or (as Bill Maher would say: new rules) give it to me in PHL 101 at the beginning of class by
10:10am.
Reading: By Wednesday we will be zipping in section 4.4 of the text.
x/y=page x, problem y in Ross.
(1) For states of the Markov chain
i,j
∈
S
, if
i
7→
j
but
j
67→
i
, then
i
is transient.
(2) Consider the gamblers ruin chain on states
{
0
,
1
,
2
,
3
,
4
}
so that if 1
≤
i
≤
3
,
p
i,i
+1
= 0
.
4
,
p
i,i

1
= 0
.
6
,
but the endpoints are absorbing:
p
00
= 1 and
p
44
= 1
.
(a) Compute
p
(3)
14
.
(b) Compute
p
(3)
10
.
(c) What is the probability that starting from state 2, there is no absorbtion for 4 moves;
that is, the game has not ended after 4 moves. (You might not want to do this by
hand.)
(3) Which states are transient and which are recurrent for the following matrices?
(
a
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This note was uploaded on 09/22/2009 for the course ORIE 3510 taught by Professor Resnik during the Summer '09 term at Cornell University (Engineering School).
 Summer '09
 RESNIK

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