Cover

Title Page

Copyright

CONTENTS

PREFACE

SPECIAL FEATURES

ABOUT THE AUTHOR

1 Probability

Introduction

1.1 Definitions of Probability

1.2 Axiomatic Definition of Probability

1.3 Conditional Probability

1.4 Marginal Probabilities

1.5 Bayes’s Theorem

1.6 Independent Events

1.7 Combinatorial Probability

Summary

Theoretical Exercises

Applied Problems

References

2 Discrete Probability Distributions

Introduction

2.1 Discrete Probability Density Function

2.2 Cumulative Distribution Function

2.3 Point Binomial Distribution

2.4 Binomial Probability Distribution

2.5 Poisson Probability Distribution

2.6 Hypergeometric Probability Distribution

2.7 Geometric Probability Distribution

2.8 Negative Binomial Probability Distribution

Summary

Theoretical Exercises

Applied Problems

References

3 Probability Distributions of Continuous Random Variables

Introduction

3.1 Continuous Random Variable and Probability Density Function

3.2 Cumulative Distribution Function of a Continuous Random Variable

3.3 Continuous Probability Distributions

Summary:Important Concepts

Theoretical Exercises

Applied Problems

References

4 Functions of a Random Variable

Introduction

4.1 Distribution of a Continuous Function of a Discrete Random Variable

4.2 Distribution of a Continuous Function of a Continuous Random Variable

4.3 Other Types of Derived Distribution

Summary

Theoretical Exercises

Applied Problems

5 Expected Values,Moments,and the Moment-Generating Function

Introduction

5.1 Mathematical Expectation

5.2 Properties of Expectation

5.3 Moments

5.4 Moment-Generating Function

Summary

Theoretical Exercises

Applied Problems

6 Two Random Variables

Introduction

6.1 Joint Probability Density Function

6.2 Bivariate Cumulative Distribution Function

6.3 Marginal Probability Distributions

6.4 Conditional Probability Density and Cumulative Distribution Functions

6.5 Independent Random Variables

6.6 Function of Two Random Variables

6.7 Expected Value and Moments

6.8 Conditional Expectations

6.9 Bivariate Normal Distribution

Summary

Theoretical Exercises

Applied Problems

7 Sequence of Random Variables

Introduction

7.1 Multivariate Probability Density Functions

7.2 Multivariate Cumulative Distribution Functions

7.3 Marginal Probability Distributions

7.4 Conditional Probability Density and Cumulative Distribution Functions

7.5 Sequence of Independent Random Variables

7.6 Functions of Random Variables

7.7 Expected Value and Moments

7.8 Conditional Expectations

Summary

Applied Problems

References

8 Limit Theorems

Introduction

8.1 Chebyshev’s Inequality

8.2 Bernoulli’s Law of Large Numbers

8.3 Weak and Strong Laws of Large Numbers

8.4 Central Limit Theorem

8.5 DeMoivre-Laplace Theorem

8.6 Normal Approximation to the Poisson Distribution

8.7 Normal Approximation to the Gamma Distribution

Summary

Applied Problems

9 Finite Markov Chains

Introduction

9.1 Basic Concepts in Markov Chains

9.2 n-Step Transition Probabilities

9.3 Evaluation of Pn

9.4 Classification of States

Applied Problems

References

List of Tables

Answers to Selected Exercises and Problems

Appendix

Index