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Math 133 Study Guide for Hour Quiz #5 C.S.Davis |
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Study Guide #5 |
Problem Set #5 |
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You are responsible for the subject matter in chapter 8 and 9. The following topics are the most important. Typical exercises from Finite Mathematics and Its Applications, eighth edition, by Goldstein/Schneider/Seigel, are assigned at the end of each objective. Work additional exercises if you need more practice. The answers to the odd numbered problems are in the back of the text. These exercises are for practice and are not graded. |
The problem set, made up of the problems below, is graded in class. See the Semester Plan for the current dates for the grading of the problem sets and taking of the hour quizzes. |
| 8.1 | 8.1 |
| 1. Given a word problem about a Markov process, determine the transition matrix and the distribution matrix for the current state. P415#1,3,5,11,15,23 | P415#10,14 |
| 8.2 | 8.2 |
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1. Given a distribution matrix for the current state
and a transition matrix for a Markov process, find a. the distribution for any future state, b. the stable distribution for the process, c. the stable matrix for the process. 2. Explain the connection between these terms: Markov process, distribution matrix, transition matrix, state, stable matrix, stable distribution. P425#1,2,5,13,17 |
P425#4,12,16,18 |
| 9.1 | 9.1 |
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1. Determine whether a matrix is a payoff matrix for
a strictly determined game or not by finding whether the payoff matrix has
a saddle point.
2. For a strictly determined game, give the optimum pure strategy (OPS) and the (expected) value of the game. P449#3,7,9,11 |
P449#4,8,10,12 |
| 9.2 | 9.2 |
| 1. For a game which is not a strictly determined game, determine which counter strategy is better for a given strategy and find the expected value of the game. P456#1,5 | P456#2 |
| 9.3 | 9.3 |
| 1. Find the optimum mixed strategy (OMS) for a not strictly determined game by solving a linear programming problem. P465#1,13 | P465#4 |