Contents

1. Introduction to Probability 2. Mathematical Probability Models 2.1 Sample Spaces and Probability 2.2 Problems on Chapter 2 3. Probability – Counting Techniques 3.1 General Counting Rules 3.2 Permutation Rules 3.3 Combinations 3.4 Problems on Chapter 3 . 4. Probability Rules and Conditional Probability 4.1 General Methods 4.2 Rules for Unions of Events 4.3 Intersections of Events and Independence 4.4 Conditional Probability 4.5 Multiplication and Partition Rules 4.6 Problems on Chapter 4 5. Review of Useful Series and Sums 5.1 Series and Sums 5.2 Problems on Chapter 5 6. Discrete Random Variables and Probability Models 6.1 Random Variables and Probability Functions . 6.2 Discrete Uniform Distribution 6.3 Hypergeometric Distribution . 6.4 Binomial Distribution 6.5 Negative Binomial Distribution 6.6 Geometric Distribution 6.7 Poisson Distribution from Binomial 6.8 Poisson Distribution from Poisson Process . 6.9 Combining Models 6.10 Summary of Single Variable Discrete Models . . 6.11 Appendix: R Software 6.12 Problems on Chapter 6

7. Expectation, Averages, Variability 7.1 Summarizing Data on Random Variables . 7.2 Expectation of a Random Variable 7.3 Some Applications of Expectation 7.4 Means and Variances of Distributions 7.5 Moment Generating Functions 7.6 Problems on Chapter 7 8. Discrete Multivariate Distributions 8.1 Basic Terminology and Techniques 8.2 Multinomial Distribution 8.3 Markov Chains . 8.4 Extension of Expectation to Multivariate Distributions . 8.5 Mean and Variance of a Linear Combination of Random Variables 8.6 Multivariate Moment Generating Functions . 8.7 Problems on Chapter 8 9. Continuous Probability Distributions 9.1 General Terminology and Notation 9.2 Continuous Uniform Distribution 9.3 Exponential Distribution 9.4 A Method for Computer Generation of Random Variables 9.5 Normal Distribution 9.6 Use of the Normal Distribution in Approximations 9.7 Problems on Chapter 9 10. Solutions to Section Problems Answers to End of Chapter Problems Summary of Distributions