Mathematics

### Material on the Final Exam

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The final exam is Thursday, December 10, 8:00 - 11:00 a.m., in the usual room.

Calculators may be used for arithmetic only.

The exam will cover Chapters 1, 4, 5 and 6 only.

For Chapters 1, 4 and 5, you can use the review sheets for Tests 1, 3 and 4. On the Test 1 review sheet, omit the Chapter 2 material.

Things you should be able to do from Chapter 6:

6.1. Tell whether a matrix is a transition matrix; write the transition matrix T from a verbal description of the situation; calculate T^2 and T^3; interpret the entries of T^k as transition probabilities after k repetitions of the process.

6.2. Write the initial probability distribution vector p_0 from a verbal description of the situation; calculate p_1, p_2 and p_3, and interpret the entries as probabilities.

6.3. Tell whether a transition matrix is regular; for a regular transition matrix, calculate the steady state vector s, and interpret the entries as long-run probabilities.

6.4. Tell whether a transition matrix is absorbing; write the transition matrix for an absorbing Markov process in canonical form (absorbing states first); for an absorbing transition matrix in canonical form, identify R and Q, calculate N and NR, interpret the entries of N and NR.

I suggest reviewing Tests 1, 3 and 4. On Test 1, omit questions 4, 5 and 6.

You may bring to the test one sheet of paper with whatever you find useful written on it. (You may use both sides of the paper if you want.)