ORIE 3510 – Homework 2
Instructor: Mark E. Lewis
due 2PM, Wednesday February 8, 2012 (ORIE Hallway drop box)
1. Give the transition diagrams for the Markov chains with the given transition matrix:
(a)
P
=
±
0
.
3 0
.
7
0
.
5 0
.
5
²
(b)
P
=
1
0
0
1
/
2
0
1
/
2
1
/
2 1
/
4 1
/
4
(c)
P
=
1
/
4 1
/
4 1
/
4 1
/
4
0
1
/
3 1
/
3 1
/
3
0
0
1
/
2 1
/
2
0
0
0
1
2. Consider an experiment in which 4 coins are tossed. Each of the coins has the probability of
0.4 of showing heads. In each step,
n
= 1
,
2
,...
, you toss the coins (among the 4 coins) that
show up as tails in the previous step. If all the coins are heads in the previous step, then you
toss all of the 4 coins. For example, if in step
n
, you see that two coins are heads and the
other two are tails, then in step
n
+1, you will toss the two coins that just showed up as tails,
leaving the head coins untouched. If, however, all the coins show up as heads in step
n
, you
toss all the four coins in step
n
+ 1. Let
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 Spring '10
 LEWIS
 Markov chain, insurance company

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