MA 114-001
Introduction to Finite Mathematics with Applications
Mathematics
Material on the Final Exam
The final exam is Monday, December 6, 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 four sheets of paper (one for each chapter) with whatever you find useful written on them. (You may use both sides of the paper if you want.) For Chapter 5 you may want to reuse the sheet you made for Test 4.
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Last modified Wed Dec 1 2004
Send questions or comments to schecter@math.ncsu.edu