8. Specify the classes of the following Markov chains, and determine whether they are transient or recurrent.

Pi =

p3 =

0 2 2 1

2 0 1 2

1 2

1 2 0 J 0 \

4 2 1

4 1

2 0 1 2

0 0 0 0 0 0 0 0 0 0 0 0 p4 =

0 0 0 1 0 0 0 1 J

1 2 0 0 0 0 1 0 1

4 3

4 0 0 0 1 2 1 2 0 0 0 0 0 1 0 0 0 0 1 3

2 3 0 1 0 0 0 0