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Contents
Preface v
Prologue vii
1 Probability 1
1.1 Properties of Probability 1
1.2 Methods of Enumeration 11
1.3 Conditional Probability 20
1.4 Independent Events 29
1.5 Bayes’ Theorem 35
2 Discrete Distributions 41
2.1 Random Variables of the Discrete Type 41
2.2 Mathematical Expectation 49
2.3 Special Mathematical Expectations 56
2.4 The Binomial Distribution 65
2.5 The Negative Binomial Distribution 74
2.6 The Poisson Distribution 79
3 Continuous Distributions 87
3.1 Random Variables of the Continuous
Type 87
3.2 The Exponential, Gamma, and Chi-Square
Distributions 95
3.3 The Normal Distribution 105
3.4* Additional Models 114
4 Bivariate Distributions 125
4.1 Bivariate Distributions of the Discrete
Type 125
4.2 The Correlation Coefficient 134
4.3 Conditional Distributions 140
4.4 Bivariate Distributions of the Continuous
Type 146
4.5 The Bivariate Normal Distribution 155
5 Distributions of Functions
of Random Variables 163
5.1 Functions of One Random Variable 163
5.2 Transformations of Two Random
Variables 171
5.3 Several Random Variables 180
5.4 The Moment-Generating Function
Technique 187
5.5 Random Functions Associated with Normal
Distributions 192
5.6 The Central Limit Theorem 200
5.7 Approximations for Discrete
Distributions 206
5.8 Chebyshev’s Inequality and Convergence
in Probability 213
5.9 Limiting Moment-Generating Functions 217
6 Point Estimation 225
6.1