MIDTERM


The midterm is a  closed book exam which will be held in class on Friday Feb 14
from 9am to 9:50 am. It will cover the sections listed on the website up to where it says

This is the end of the sections covered by the midterm


Don't try to read everything in the book; use your class notes as
a guide and the book as an aid to understanding what is not clear in my notes.
I tend to give more complete proofs but you may find explanations in the book more helpful.
I have been telling you lots of things and the plot may not be clear, but when you go over it all
you are doing well if it suddenly starts to fit together.

Go over the solutions to homework comparing mine and yours.  I like to base midterm problems on homework.
Our marker does the best she can with the time she has but she is not going to notice every mistake. Unfortunately I
will be marking your exam (with her help) and I might notice every mistake.

There will be four questions. Each may have several parts and some parts will be
about theory.

Examples of typical theory parts of questions are:

What is the equation that defines the Markov property?
( P(X_{n+1}=j|X_n=i, ......) = P(X_{n+1}=j|X_n=i) )

What conditions imply that the matrix elements of P^n have limits as n -> infinity
(theorem 4.1, know what the terms in it mean)

Give an example of a Markov chain such that the matrix elements of P^n do not
have limits as n -> infinity
(Zerox machine example with probability one for changing state)

What equation does a stationary probability distribution satisfy
(pi P = pi)

What are the equations of detailed balance
(pi_i P_ij = pi_j P_ji for all states i,j)

Does stationary imply detailed balance or is it the other way round
(other way round)

Along the way in class I have thrown out little hints about what I would like you to
know how to prove.  Also there will be questions with a problem to solve.

In mathematics it is important to learn definitions well.  I have posted a little note on our webpage with
some definitions in it that might be hard to extract from the book.







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