1. Consider the game of chess. Assume your opponent is the "environment" and their actions follow some probability distribution for each position they encounter. Briefly discuss whether playing chess can be modeled as a Markov Decision Process. 2. Let be a possibly probabilistic policy mapping each state s in an MDP to a (probability distribution of) actions. 2a) Express v(s) in terms of q. 2b) Express q(s,a) in terms of v. 2c) Express the optimal v(s) in terms of q. 2d) Express the optimal q(s,a) in terms of v