Consider the following Markov chain: a) For which values of the parameters p and q is the Markov chain irreducible? For the rest of the problem, consider only the cases in which the Markov chain is irreducible. b) Calculate the entropy rate of the Markov chain as a function of the parameters p and q. c) For which values of the parameters p and q does the Markov chain achieve the minimum entropy? Give the value of the entropy. d) Is the maximum entropy rate of the Markov chain greater or less than 1 ? e) Assume q=1. For which value of p does the Markov chain achieve the maximum entropy? Note: Express this value as a solution of an algebraic equation..