midterm06sol - STAT 455/855 Solutions: Midterm Fall, 2006...

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STAT 455/855 – Solutions: Midterm Fall, 2006 1. (a) Yes. Examples are a random walk on the vertices of a square (or any polygon with an even number of sides), or the random walk with reflecting barrier at 0 described in problem 2, both of which have period 2 and are time reversible. (b) No. If a state is null recurrent then the class containing it is closed since recurrent classes are closed. So we can restrict the state space to this class and we know the stationary distribution on this class exists and is unique with all positive entries, and given by the inverses of the mean recurrence times to states. Hence all mean recurrence times are finite and so all states must be positive recurrent. (c) No. If you leave a transient state i and go to a state k that is outside of the class of state i , then return back to the class of i , once you are back in the class of i , it must be possible to get back to state i since all states in the class of i communicate with i , by definition. Hence state
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This note was uploaded on 09/15/2010 for the course STAT 455/855 taught by Professor Glentakahara during the Fall '09 term at Queens University.

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midterm06sol - STAT 455/855 Solutions: Midterm Fall, 2006...

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