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

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Chapter1: Combinatorial Analysis
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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
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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