This is a text tor a one-quaaer or one-semester course in probability．aimed at stu．dents who have done a year of calculus．The book is organized so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus．Later chapters develop these ideas further using calculus tools．The book contains more than the usual number of examples worked out in detail．

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

　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