1 Preface
1 Introduction
1.1 Equally Likely Outcomes
1.2 Interpretations
1.3 Distributions
1.4 Conditional Probability and Independence
1.5 Bayes Rule
1.6 Sequences of Events
Summary
2 Review Exercises
2 Repeated Trials and Sampling
2.1 The Binomial Distribution
2.2 Normal Approximation： Method
2.3 Normal Approximation： Derivation (Optional)
2.4 Poisson Approximation
2.5 Random Sampling
Summary
Review Exercises
3 Random Variables
3.1 Introduction
3.2 Expectation
3.3 Standard Deviation and Normal Approximation
3.4 Discrete Distributions
3.5 The Poisson Distribution
3.6 Symmetry (Optional)
Summary
Review Exercises
4 Continuous Distributions
4.1 Probability Densities
4.2 Exponential and Gamma Distributions
4.3 Hazard Rates (Optional)
4.4 Change of Variable
4.5 Cumulative Distribution Functions
4.6 Order Statistics (Optional)
Summary
Review Exercises
5 Continuous Joint Distributions
5.1 Uniform Distributions
5.2 Densities
5.3 Independent Normal Variables
5.4 Operations (Optional)
Summary
Review Exercises
6 Dependence
6.1 Conditional Distributions： Discrete Case
6.2 Conditional Expectation： Discrete Case
6.3 Conditioning： Density Case
6.4 Covariance and Correlation
6.5 Bivariate Normal
Summary
Review Exercises
Distribution Summaries
Discrete
Continuous
Beta
Binomial
Exponential
Gamma
Geometric and Negative Binomial
Hypergeometric
Normal
Poisson
Uniform
Examinations
Solutions to Examinations
Appendices
1.Counting
2.Sums
3.Calculus
4.Exponents and Logarithms
5.Normal Table
Brief Solutions to Odd-Numbered Exercises
Index
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