1. (a) For the 4-state Markov process whose transition matrix is given by 1/2 1/2 0 0 2/3 0 0 1/3 0 U 4 / 5 1/5 " 1 U U 0 draw the associated directed graph and identify which states are recurrent, transient and absorbing. (1)) Determine if the process is irreducible and if so, is it aperiodic? 2. Labelling the rows of the matrix in 1(a) as corresponding to the states 0, 1, 2, and 3 respectively, calculate the probabilities fm, f11, f21 and f31 for the 4-state Markov process in Question 1