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Show transcribed image text Consider a standard chessboard with an 8 Ã— 8 grid of possible locations. We define a Markov chain by randomly moving a single chess piece on this board. The initial location Xo is sampled u sampling uniformly from the set of legal moves given its current location Xt. For a description of legal chess moves, see: http://en.wikipedia.org/wiki/Rules-of-chess#Basic-moves. niformly among the 82-64 squares. At time t, the piece then chooses X by a) Suppose the chess piece is a king, which can move to any of the 8 adjacent squares. Is the Markov chain irreducible? Is the Markov chain aperiodic? b) Suppose the chess piece is a bishop. Is the Markov chain irreducible? Is the Markov chain aperiodic? c) Suppose the chess piece is a knight. Is the Markov chain irreducible? Is the Markov chain aperiodic?

Consider a standard chessboard with an 8 Ã— 8 grid of possible locations. We define a Markov chain by randomly moving a single chess piece on this board. The initial location Xo is sampled u sampling uniformly from the set of legal moves given its current location Xt. For a description of legal chess moves, see: http://en.wikipedia.org/wiki/Rules-of-chess#Basic-moves. niformly among the 82-64 squares. At time t, the piece then chooses X by a) Suppose the chess piece is a king, which can move to any of the 8 adjacent squares. Is the Markov chain irreducible? Is the Markov chain aperiodic? b) Suppose the chess piece is a bishop. Is the Markov chain irreducible? Is the Markov chain aperiodic? c) Suppose the chess piece is a knight. Is the Markov chain irreducible? Is the Markov chain aperiodic?