# HW2 - Math 526 003 Winter 2017 Assignment#2 Due date...

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Math 526 - 003 – Winter 2017 - Assignment #2 Due date: Thursday 2/16/2017 No Later than 3:00pm . You can hand in your work during class or put your solution in the box on my office door (EH 4839). You can use a calculator or a computer program to perform some of the calculations. Please indicate this explicitly in your solution. The maximum number of points you can receive for this homework is 12 . Problem 1 (3 points) . Consider 8 ˆ 8 chess board. A bishop can move any number of squares diagonally. Let p X n q be the sequence of squares that results if we pick one of bishop’s legal moves at random. a) Find the stationary distribution of p X n q (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 p 1 , 1 q when we start there. (Hint: there is a formula that connects the desired quantity to stationary distribution, but it only holds for irreducible Markov chains!) Problem 2 (2 points) . A fair coin is tossed repeatedly. Let us denote heads by H