Question: Kings random walk. This and the next example continue Example 1.30. A king can move one squares horizontally, vertically, or diagonally. Let Xn be the

King’s random walk. This and the next example continue Example 1.30. A king can move one squares horizontally, vertically, or diagonally. Let Xn be the sequence of squares that results if we pick one of king’s legal moves at random.

Find

(a) the stationary distribution and

(b) the expected number of moves to return to corner (1,1) when we start there.

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