Handbook of Probability

THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY

Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability.

The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introduction, historical background, theory and applications, algorithms, and exercises. The Handbook of Probability offers coverage of:

• Probability Space
• Probability Measure
• Random Variables
• Random Vectors in Rⁿ
• Characteristic Function
• Moment Generating Function
• Gaussian Random Vectors
• Convergence Types
• Limit Theorems

The Handbook of Probability is an ideal resource for researchers and practitioners in numerous fields, such as mathematics, statistics, operations research, engineering, medicine, and finance, as well as a useful text for graduate students.

Table of Contents

Chapter One: Probability Space
Chapter Two: Probability Measure
Chapter Three: Random Variables: Generalities
Chapter Four: Random Variables: the Discrete Case
Chapter Five: Random Variables: the Continuous Case
Chapter Six: Generating Random Variables
Chapter Seven: Random Vectors in Rn
Chapter Eight: Characteristic Function
Chapter Nine: Moment-generating Function
Chapter Ten: Gaussian Random Vectors
Chapter Eleven: Convergence Types. Almost Sure Convergence. Lp-convergence. Convergence in Probability
Chapter Twelve: Limit Theorems
Chapter Thirteen: Appendix A: Integration Theory. General Expectations
Chapter Fourteen: Appendix B: Inequalities Involving Random Variables and Their Expectations