Consider a Markov Chain with the following state diagram. 2 0.2 0.4 0.1 0.1 3 5 0.4 0.1 0.1 0.1 0.2 0.2 0.2 6 0.1 0.1 8 0.3 i) How many linearly independent equilibrium distributions exist for this system? Justify your answer. ii) Write down each of these possible equilibrium distributions along with a clear explanation of how you obtained them. Your justification could be calculation of a vector of probabilities or it could be a written explanation of the possible behaviour of the chain. Give your answers as probability vectors i.e. Meg = (wl 12 13 14 15 1 1 178 1 ) where each w is the equilibrium probability that the chain is in state j