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Concepts of Probability Theory: Second Revised Edition (Dover Books on Mathematics)

by

Concepts of Probability Theory: Second Revised Edition (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

This approach to the basics of probability theory employs the simple conceptual framework of the Kolmogorov model, a method that comprises both the literature of applications and the literature on pure mathematics. The author also presents a substantial introduction to the idea of a random process. Intended for college juniors and seniors majoring in science, engineering, or mathematics, the book assumes a familiarity with basic calculus.

After a brief historical introduction, the text examines a mathematical model for probability, random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. Problems with answers conclude each chapter, and six appendixes offer supplementary material. This text provides an excellent background for further study of statistical decision theory, reliability theory, dynamic programming, statistical game theory, coding and information theory, and classical sampling statistics.

Synopsis:

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduate students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

Synopsis:

Mathematical model for probability, random variables, probability distributions, mathematical expectation, random processes, etc.

Synopsis:

Using Kolmogorov model, book discusses random variables, probability distributions, mathematical expectation, random processes, etc. For college juniors, seniors in science, engineering or math. Problems with answers. 6 appendices. Intermediate level.


Synopsis:

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

Table of Contents

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 Processes

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

Product Details

ISBN:
9780486636771
Author:
Pfeiffer, Paul E.
Publisher:
Dover Publications
Author:
Pfeiffer, Paul E.
Author:
Mathematics
Location:
New York :
Subject:
Mathematics
Subject:
Statistics
Subject:
Probability
Subject:
Probabilities
Subject:
Probability & Statistics - General
Subject:
General Mathematics
Subject:
Probability Theory.
Subject:
Kolmogorov model
Subject:
random process
Subject:
Mathematics | Probability and Statistics
Copyright:
Edition Number:
2
Edition Description:
Second Edition, Revised
Series:
Dover Books on Mathematics
Publication Date:
20120631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
416
Dimensions:
8.25 x 5.63 in 1 lb

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Related Subjects


Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Probability Theory
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Concepts of Probability Theory: Second Revised Edition (Dover Books on Mathematics) Used Trade Paper
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Product details 416 pages Dover Publications - English 9780486636771 Reviews:
"Synopsis" by ,
Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduate students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.
"Synopsis" by , Mathematical model for probability, random variables, probability distributions, mathematical expectation, random processes, etc.

"Synopsis" by , Using Kolmogorov model, book discusses random variables, probability distributions, mathematical expectation, random processes, etc. For college juniors, seniors in science, engineering or math. Problems with answers. 6 appendices. Intermediate level.


"Synopsis" by ,
Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.
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