Statistics 251/551 spring 2013
2013: Solutions to sheet 1
[1]
(5 points) Suppose X0 , X1 , . . . is a Markov chain with state space S and transition probabilities P (i, j ) for i, j S. Dene Yn = X2n . Show that Y0 , Y1 , . . . is also a Markov chain,
with
Statistics 251/551 spring 2013
2013: Solutions to sheet 2
If you are not able to solve a part of a problem, you can still get credit for later
parts: Just assume the truth of what you were unable to prove in the earlier part.
[1]
Consider an irreducible M
Statistics 251/551 spring 2013
2013: Solutions to sheet 3
If you are not able to solve a part of a problem, you can still get credit for later
parts: Just assume the truth of what you were unable to prove in the earlier part.
[1]
(10 points) Find the tran
1
Statistics 251/551 spring 2013
2013: Solutions to sheet 4
This homework will step you through the proof of Lemma 1 in the Jerrum
(1995) paper.1 I mostly use Jerrums notation, except that the number of colors
is q , not k .
The setting
The set of availab
Statistics 251/551 spring 2013
2013: Solutions to sheet 5
If you are not able to solve a part of a problem, you can still get credit for later
parts: Just assume the truth of what you were unable to prove in the earlier part.
[1]
Suppose and are stopping
Statistics 251/551 spring 2013
2013: Solutions to sheet 6
If you are not able to solve a part of a problem, you can still get credit for later
parts: Just assume the truth of what you were unable to prove in the earlier
part.
[1]
(15 points) Suppose
(a) S