I'm only seeking help for 1.15.

1.8 is just to provide the information you need to solve 1.15. Thank you for your help!

1.15. Find limn >co p" (i, j) for the chains in parts (c), (d), and (e) of Problem 1.8.1.8. Consider the following transition matrices. Identify the transient and recurrent states, and the irreducible closed sets in the Markov chains. Give reasons for your answers. (b)123456 (\"\"2345 1.100.450 1.4.3.300 2.1.2.2050 20.50.50 30.1.3005 3.50.500 4.100.900 40.50.50 503034 5000.405 ' " 6000055 (012345 (d)123456 1.800.200 100001 20.500.50 20.20.80 300.3.4.1.2 3.1.2.4.30 4.100.900 40.40.60 520008 50.200.80 ' ' 60.30.30.4 (e)1 2 3 4 5 110 0 0 0 2 02/301/30 3 1/81/45/8 0 0 4 0 1/6 0 5/6 0 5 1/3 0 1/3 0 1/3