On an empty NxN chessboard, a knight starts from a point (say location x, y) and it starts moving randomly, but once it moves out of board, it can’t come inside.
(1) What is the total probability that it stays within the board after N steps?
(2) What is the expected number of steps before it steps out?
(1) What is the total probability that it stays within the board after N steps?
(2) What is the expected number of steps before it steps out?