Consider a Markov Chain {X,, X2, X3,...} with transition matrix 0.1 01 0.3 0.5 0 0 0.2 0.2 0.15 0.15 0.15 0.15 0 0.3 0 0.3 0.4 0 P = 0.5 0.1 0.1 0.1 0.1 0.1 0 0.4 0 0 0 0.6 0.1 0.1 0.2 0.3 0.2 0.1 i) Draw the state diagram for this chain, labelling all possible transitions with directed arrows with appropriate weights. i) Assume that the states are labelled 1, 2, 3, 4, 5 and 6 and that the ith row, jth column entry of P gives gives P(X,. = j|X, = i). Calculate P(X, 2 = 5 X, = 2). iic) Find the equilibrium distribution of this chain /7 such that n P = neg - Hint: You might wish to use a mathematical package to find the eigenvectors of pt