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.
number of points you can receive for this homework is
8 chess board. A bishop can move any number of squares
be the sequence of squares that results if we pick one of bishop’s legal
moves at random.
a) Find the stationary distribution of
(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
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!)
A fair coin is tossed repeatedly. Let us denote heads by