Information about Mid-term Test, April 2, 2007
==============================================

During the Spring Break, I will post a list of specific topics to
study for the Midterm test, and will give links to sample problems.

Here are a selection of topics on which I will base 
test questions. A separate sheet of sample problems
can be found in "SampTst07.pdf" in the same directory 
as this page.

(1) Calculation using conditional expectations, especially in: 
    (A) "First-step analysis", and 
    (B) Wald's Lemma.

(2) Definition and basic consequences of Markov Property, 
including:
    (A) checking that a process is NOT an HMC
    (B) using Theorem 2.1 or 2.2 to show that a process IS an HMC.

(3) Probabilities of absorption, expected time to absorption,
using first-step analysis.

(4) Classification of states in a HMC. Checking irreducibility,
aperiodicity. Equivalent conditions for (each of) irreducibility 
and aperiodicity.

(5) Invariant vector x_i. Criteria for positive recurrence including
explicit calculation of ET_0 and use of reversibility.

(6) Calculation of long-term average quantities for Markov chains,
when expressed in terms of functions on cycles between successive
visits to some state. 

(7) Definition and application of Strong Markov Property.

YOU WILL NOT BE RESPONSIBLE FOR REPRODUCING PROOFS OF THEOREMS,
BUT RATHER FOR UNDERSTANDING AND USING THE RESULTS OF THOSE 
THOEREMS IN CONCRETE EXAMPLES.