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Larsen, Richard and Marx, Morris, “An introduction to mathematical statistics and its applications”, 5th edition, Prentice Hall

1.4 A Chapter Summary 14

2 Probability 16

2.1 Introduction 16

2.2 Sample Spaces and the Algebra of Sets 18

2.3 The Probability Function 27

2.4 Conditional Probability 32

2.5 Independence 53

2.6 Combinatorics 67

2.7 Combinatorial Probability 90

2.8 Taking a Second Look at Statistics (Monte Carlo Techniques) 99

3 Random Variables 102

3.1 Introduction 102

3.2 Binomial and Hypergeometric Probabilities 103

3.3 Discrete Random Variables 118

3.4 Continuous Random Variables 129

3.5 Expected Values 139

3.6 The Variance 155

3.7 Joint Densities 162

3.8 Transforming and Combining Random Variables 176

3.9 Further Properties of the Mean and Variance 183

3.10 Order Statistics 193

3.11 Conditional Densities 200

3.12 Moment-Generating Functions 207

3.13 Taking a Second Look at Statistics (Interpreting Means) 216

Appendix 3.A.1 Minitab Applications 218