4. (20 points) Suppose that the three states of a system are represented by a random variable X that can take one of three values, and the state transition is modeled as a Markov process with a transition matrix given by 0.8 0.2 0 P = 0.4 0.3 0.3 0 0.6 0.4 a) (10 Points) Find the stationary distribution of the Markov chain, u b) (10 Points) Calculate the entropy rate H(X) of this process