chap1_2 - 2007 edition ii Contents 1. Introduction to...

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Unformatted text preview: 2007 edition ii Contents 1. Introduction to Probability 1 2. Mathematical Probability Models 5 2.1 Sample Spaces and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Problems on Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3. Probability Counting Techniques 15 3.1 General Counting Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Permutation Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.4 Problems on Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4. Probability Rules and Conditional Probability 29 4.1 General Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Rules for Unions of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3 Intersections of Events and Independence . . . . . . . . . . . . . . . . . . . . . . . . 35 4.4 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.5 Multiplication and Partition Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.6 Problems on Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5. Review of Useful Series and Sums 51 5.1 Series and Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2 Problems on Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6. Discrete Random Variables and Probability Models 55 6.1 Random Variables and Probability Functions . . . . . . . . . . . . . . . . . . . . . . . 55 6.2 Discrete Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.3 Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 iii iv 6.4 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.5 Negative Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.6 Geometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.7 Poisson Distribution from Binomial . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.8 Poisson Distribution from Poisson Process . . . . . . . . . . . . . . . . . . . . . . . . 73 6.9 Combining Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.10 Summary of Single Variable Discrete Models . . . . . . . . . . . . . . . . . . . . . . 80 6.11 Appendix: R Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.12 Problems on Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7. Expectation, Averages, Variability 93 7.1 Summarizing Data on Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . 93 7.2 Expectation of a Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . .Expectation of a Random Variable ....
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chap1_2 - 2007 edition ii Contents 1. Introduction to...

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