For a certain group of states, it was observed that 70% of the Democratic governors were succeeded by Democrats and 30% by Republicans. Also, 40% of the Republican governors were succeeded by Democrats and 60% by Republicans.
(a) Set up the 2 × 2 stochastic matrix with columns and rows labeled D and R that displays these transitions.
(b) Compute A2 and A3.
(c) Suppose that all current governors are Democrats. Assuming that the current trend holds for three elections, what percent of the governors will then be Democrats?