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by Ciprian A. Tudor, Ionut Florescu
Handbook of Probability
Cover
Wiley Handbooks in Applied Statistics
Title Page
Copyright
List of Figures
Preface
Introduction
Chapter One: Probability Space
1.1 Introduction/Purpose of the Chapter
1.2 Vignette/Historical Notes
1.3 Notations and Definitions
1.4 Theory and Applications
1.5 Summary
Exercises
Chapter Two: Probability Measure
2.1 Introduction/Purpose of the Chapter
2.2 Vignette/Historical Notes
2.3 Theory and Applications
2.4 Lebesgue Measure on the Unit Interval (0,1]
Exercises
Chapter Three: Random Variables: Generalities
3.1 Introduction/Purpose of the Chapter
3.2 Vignette/Historical Notes
3.3 Theory and Applications
Exercises
Chapter Four: Random Variables: The Discrete Case
4.1 Introduction/Purpose of the Chapter
4.2 Vignette/Historical Notes
4.3 Theory and Applications
4.4 Examples of Discrete Random Variables
Exercises
Chapter Five: Random Variables: The Continuous Case
5.1 Introduction/Purpose of the Chapter
5.2 Vignette/Historical Notes
5.3 Theory and Applications
5.4 Examples
Exercises
Chapter Six: Generating Random Variables
6.1 Introduction/Purpose of the Chapter
6.2 Vignette/Historical Notes
6.3 Theory and Applications
6.4 Generating Multivariate Distributions with Prescribed Covariance Structure
Exercises
Chapter Seven: Random Vectors in Rn
7.1 Introduction/Purpose of the Chapter
7.2 Vignette/Historical Notes
7.3 Theory and Applications
Exercises
Chapter Eight: Characteristic Function
8.1 Introduction/Purpose of the Chapter
8.2 Vignette/Historical Notes
8.3 Theory and Applications
8.4 Calculation of the Characteristic Function for Commonly Encountered Distributions
Exercises
Chapter Nine: Moment-Generating Function
9.1 Introduction/Purpose of the Chapter
9.2 Vignette/Historical Notes
9.3 Theory and Applications
Exercises
Chapter Ten: Gaussian Random Vectors
10.1 Introduction/Purpose of the Chapter
10.2 Vignette/Historical Notes
10.3 Theory and Applications
Exercises
Chapter Eleven: Convergence Types. Almost Sure Convergence. Lp-Convergence. Convergence in Probability
11.1 Introduction/Purpose of the Chapter
11.2 Vignette/Historical Notes
11.3 Theory and Applications: Types of Convergence
11.4 Relationships Between Types of Convergence
Exercises
Chapter Twelve: Limit Theorems
12.1 Introduction/Purpose of the Chapter
12.2 Vignette/Historical Notes
12.3 Theory and Applications
12.4 Central Limit Theorem
Exercises
Chapter Thirteen: Appendix A: Integration Theory. General Expectations
13.1 Integral of Measurable Functions
13.2 General Expectations and Moments of a Random Variable
Chapter Fourteen: Appendix B: Inequalities Involving Random Variables and Their Expectations
14.1 Functions of Random Variables. The Transport Formula
Bibliography
Index
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