Question 3: Consider a Markov Chain (X)n20 on {1, 2, 3} with transition matrix P. Suppose that P = ( 1 2p 2p 0 0 P 1-2p 2p 1-2p D) (a) Draw a diagram and also identify a condition in which no state is absorbing. (b) Suppose no state is absorbing, calculate the general form of in terms of p. (c) Suppose no state is absorbing, using (b) to find the invariant distribution for state 1, i.e.41, and provide a brief argument. (d) Calculate the invariant distribution (to confirm your answer in (c)). (e) Find the mean recurrence time of state 1.