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Unformatted text preview: MATH 1711 FINAL EXAM STUDY GUIDE In studying for the final exam, you should FIRST study all tests and quizzes we have had this semester. Just a reminder: solutions to all tests and quizzes can be found on T-square. Then go over old homework problems and examples we have done in class. The following list contains all the topics that will be covered on the final exam (if a topic is not on this list, it wont be on the final!): Gauss-Jordan Elimination (2.1, 2.2) Inverting a Matrix (2.4,2.5) The Multiplication and Addition Rules (5.4) Combinations and Permutations (5.5, 5.6) Binomials and Multinomials (5.7, 5.8) Probability Using Counting (6.3, 6.4) Conditional Probability and Independence (6.5) Binomial Probability (7.3) Expected Value (Mean) (7.4) Markov ChainsStable Distributions (8.1, 8.2) Markov ChainsAbsorbing Matrices (8.3) Game TheoryPure and Mixed Strategies (9.1, 9.2, 9.3) Interest and Annuities (10.1, 10.2, 10.3) The next page contains some practice problems. Try to work them by yourself without using your book or notes. The TAs will NOT discuss the solutions in recitation, but you may ask us about the problems in office hours or at the review session. Practice Problems 1. An urn contains three white balls and two red balls. The balls are drawn from the urn, one at a time without replacement, until a white ball is drawn. Let X be the number of the draw on which a white ball is drawn for the first time. Find the expected value of X . 2. Find A 1 if A is the matrix 1 4 2 0 2 1 3 5 3 ....
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- Spring '08