a) Find the steady-state probabilities for each of the Markov chains in Figure 4.2. Assume that all clockwise probabilities in the first graph are the same, say p, and assume that P 4,5 = P 4,1 in the...

a) Find the steady-state probabilities for each of the Markov chains in Figure 4.2. Assume that all clockwise probabilities in the first graph are the same, say p, and assume that P_4,5
= P_4,1
in the second graph.

b) Find the matrices [P²] for the same chains. Draw the graphs for the Markov chains represented by [P²], i.e., the graph of two step transitions for the original chains. Find the steady-state probabilities for these two step chains. Explain why your steady-state probabilities are not unique.

c) Find lim_n→1[P²ⁿ] for each of the chains.