Concepts of Probability theory

Paul E. Pfeiffer

Publisher:

Dover Publications

Publication Date:

1978

Number of Pages:

405

Format:

Paperback

Edition:

2

Price:

15.95

ISBN:

9780486636771

Category:

Textbook

MAA Review
Table of Contents

We do not plan to review this book.

Preface
Chapter 1. Introduction
1-1. Basic Ideas and the Classical Definition
1-2. Motivation for a More General Theory
Selected References
Chapter 2. A Mathematical Model for Probability
2-1. In Search of a Model
2-2. A Model for Events and Their Occurrence
2-3. A Formal Definition of Probability
2-4. An Auxiliary Model-Probability as Mass
2-5. Conditional Probability
2-6. Independence in Probabililty Theory
2-7. Some Techniques for Handling Events
2-8. Further Results on Independent Events
2-9. Some Comments on Strategy
Problems
Selected References
Chapter 3. Random Variables and Probability Distributions
3-1. Random Variables and Events
3-2. Random Variables and Mass Distributions
3-3. Discrete Random Variables
3-4. Probability Distribution Functions
3-5. Families of Random Variables and Vector-valued Random Variables
3-6. Joint Distribution Functions
3-7. Independent Random Variables
3-8. Functions of Random Variables
3-9. Distributions for Functions of Random Variables
3-10. Almost-sure Relationships
Problems
Selected References
Chapter 4. Sums and Integrals
4-1. Integrals of Riemann and Lebesque
4-2. Integral of a Simple Random Variable
4-3. Some Basic Limit Theorems
4-4. Integrable Random Variables
4-5. The Lebesgue-Stieltjes Integral
4-6. Transformation of Integrals
Selected References
Chapter 5. Mathematical Expectation
5-1. Definition and Fundamental Formulas
5-2. Some Properties of Mathematical Expectation
5-3. The Mean Value of a Random Variable
5-4. Variance and Standard Deviation
5-5. Random Samples and Random Variables
5-6. Probability and Information
5-7. Moment-generating and Characteristic Functions
Problems
Selected References
Chapter 6. Sequences and Sums of Random Variables
6-1. Law of Large Numbers (Weak Form)
6-2. Bounds on Sums of Independent Random Variables
6-3. Types of Convergence
6-4. The Strong Law of Large Numbers
6-5. The Central Limit Theorem
Problems
Selected References
Chapter 7. Random Processes
7-1. The General Concept of a Random Process
7-2. Constant Markov Chains
7-3. Increments of Processes; The Poisson Process
7-4. Distribution Functions for Random Processes
7-5. Processes Consisting of Step Functions
7-6. Expectations; Correlation and Covariance Functions
7-7. Stationary Random Proc
7-8. Expectations and Time Averages; Typical Functions
7-9. Gaussian Random Processes
Problems
Selected References
Appendixes
Appendix A. Some Elements of Combinatorial Analysis
Appendix B. Some Topics in Set Theory
Appendix C. Measurability of Functions
Appendix D. Proofs of Some Theorems
Appendix E. Integrals of Complex-valued Random Variables
Appendix F. Summary of Properties and Key Theorems
BIBLIOGRAPHY
INDEX