Suggest 8 × 8 chess board. A bishop can move any number of squares diagonally. Let (Xn) be sequence of squares that results if we pick one of bishops legal moves at random.
a) Find a stationary distribution of (Xn) (you can represent the answer by drawing a chess board and writing numbers in the cells).
b) Find the expected number of moves to return to corner (1, 1) when we start there