(Solved): On the fictional island of Westeros, the four great houses (House Targaryen, House Stark, House Ba ...

On the fictional island of Westeros, the four great houses (House Targaryen, House Stark, House Baratheon and House Lannister) are in an eternal power struggle for the Iron Throne. You are working for the Westerosequivalent of FiveThirtyEight, and it is your task to determine for each house the long term probability that one of their members sits on the Iron Throne. Nate Silver already told you that the transition probabilities from one year to the next are given by the following Markov chain: 1) Compute the $$4\times 4$$-matrix transition matrix $$T$$ for the above Markov chain. Sort the columns as follows: House Targaryen, House Stark, House Baratheon, and House Lannister. Store this matrix as markov_matrix. 2) Compute the steady state vector of this system; that is, find a probability vector which is an eigenvector of $$T$$ with eigenvalue 1 . Save this as steady_state. 3) Suppose a member of House Targaryen currently sits on the Iron Throne. What is the probability that a member of House Stark sits on the throne in exactly three years? Save this as prob_stark. $$Y_1$$