1. Given the following (one-step) transition matrices of a Markov chain (MC), draw the state transition diagram for each MC, determine the classes of the MC and, for each class determine whether it is recurrent or transient. (a) P = (d) P = [0 0 1 1 2 0 0 1 0 0 0 0 0 0 0 0 1 4 (b) P = (e) P = 0 1 0 LO 0 0 0 1 1 3 0 2 2 3 0 0 0 0 3 00 1 0 0 0 1 0 00 0 0 0 00 0 0 0 0 0- 1 0 0 0 0 (c) P (f) P 0 0 0 0 0- 1 0 0 0 0 0 1 0 3 10 1 1 3 0
1. Given the following (one-step) transition matrices of a Markov chain (MC), draw the state transition diagram for each MC, determine the classes of the MC and, for each class determine whether it is recurrent or transient. (a) P = (d) P = [0 0 1 1 2 0 0 1 0 0 0 0 0 0 0 0 1 4 (b) P = (e) P = 0 1 0 LO 0 0 0 1 1 3 0 2 2 3 0 0 0 0 3 00 1 0 0 0 1 0 00 0 0 0 00 0 0 0 0 0- 1 0 0 0 0 (c) P (f) P 0 0 0 0 0- 1 0 0 0 0 0 1 0 3 10 1 1 3 0
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question

Transcribed Image Text:1.
Given the following (one-step) transition matrices of a Markov chain (MC), draw the state transition
diagram for each MC, determine the classes of the MC and, for each class determine whether it is
recurrent or transient.
(a) P
(d) P
=
=
O WITHIWAIN
1
2 2
1
BILALIM O
3
4
1
0
3 3
000
O WIT O
0
3
1
0
0 0
000
0
00
0
3|14|w
0
1434
(b) P=
(e) P
=
00
1
0
LO
OTO O
0
T10
0
0
0 0
NITOITOOO
00
13000
NIMOOO
2
1 0 0
1
2
3
O LO OLO
NIMO O OOO
1
0
0
0-
3
0 0
0 0 0
0
OOO MITOLIN
00
0 0
3
LI3OO
4
2
(c) P
(f) P
=
0
0 112
O
WITO O DIA
0
OLIZLIN O
00
2
0 0
415
- NTNITO
O ONIT
O
120
0113
0-
NIE
WITTHTATEGIE
10
NISO O
0
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