PROBLEM 7 Consider a two-state Markov chain. Suppose that each state i E {1, 2} offers with the following two choices of rewards r. and transition probabilities PC and P?): r1) = 5, (3) (4) (2) = 1, r) = 2, P} [ 0.1 0.9 ] P??? = [ 0.5 0.5 ] p.) = [ 0.1 0.9] P? = [ 0.5 0.5 ] (5) |(2) = 1, 1 2 (6) Using dynamic programming, compute the optimal policy d; (h) that maximizes expected aggregate reward vi (h) from times m to m+h, E {1, 2}, for h 1. Report also v (1) for i E {1,2}. = PROBLEM 7 Consider a two-state Markov chain. Suppose that each state i E {1, 2} offers with the following two choices of rewards r. and transition probabilities PC and P?): r1) = 5, (3) (4) (2) = 1, r) = 2, P} [ 0.1 0.9 ] P??? = [ 0.5 0.5 ] p.) = [ 0.1 0.9] P? = [ 0.5 0.5 ] (5) |(2) = 1, 1 2 (6) Using dynamic programming, compute the optimal policy d; (h) that maximizes expected aggregate reward vi (h) from times m to m+h, E {1, 2}, for h 1. Report also v (1) for i E {1,2}. =