= 2. The Bishop's Random Walk. See an example of a chess board at the end...

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= 2. The Bishop's Random Walk. See an example of a chess board at the end of the file. The Bishop may move 1-7 squares in any diagonal direction. Let X be the sequence of squares that the bishop visits as it moves randomly across the board starting from A8 (E.G., Xo A8, X = G2, X2 = F1). The bishop cannot stay still and must move to another square at every n. Find: (a) the stationary distribution of X, and (b) the expected number of moves to return to corner A8 when we start there. (7+714 points) = 2. The Bishop's Random Walk. See an example of a chess board at the end of the file. The Bishop may move 1-7 squares in any diagonal direction. Let X be the sequence of squares that the bishop visits as it moves randomly across the board starting from A8 (E.G., Xo A8, X = G2, X2 = F1). The bishop cannot stay still and must move to another square at every n. Find: (a) the stationary distribution of X, and (b) the expected number of moves to return to corner A8 when we start there. (7+714 points)