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IEOR 161
University of California, Berkeley
Spring 2010
Homework 7
Due date:
April 2 (in discussion session), 2010.
The following are taken from “Introduction to Probability Models” by Sheldon Ross (
9th Edi
tion
).
1. 5.67, 5.72
2. 4.2, 4.3, 4.8
3. Consider a birthdeath process with
p
i,i
+1
=
u, p
i,i

1
=
d, p
i,i
= 1

u

d,
for
i
≥
1
and
p
0
,
1
=
u, p
0
,
0
= 1

u

d.
•
Simulate 10000 sample paths of this Markov chain starting at
x
(0) = 0 with
u
=
0
.
35
,d
= 0
.
55. For each simulation run, record the state of the Markov chain at time
t
= 5
,
10
,
20
,
50
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Unformatted text preview: , 75 , 100 , 200. Once the 10000 sample runs have all been generated, plot histograms of the distribution of the state for each of these times. (Normalize the histograms so that they represent a probability mass function). Explain in words what these histograms represent. • Plot the histogram of a geometric random variable with success probability p = 1( u/d ). How does this compare with the histograms you have just constructed? 1...
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This note was uploaded on 03/17/2011 for the course IEOR 161 taught by Professor Lim during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Lim
 Operations Research

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