Lukacs Probability and Mathematical Statistics

An Introduction
1. Auflage 2014
ISBN: 978-1-4832-6920-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 254 Seiten, Web PDF

Probability and Mathematical Statistics: An Introduction provides a well-balanced first introduction to probability theory and mathematical statistics. This book is organized into two sections encompassing nine chapters. The first part deals with the concept and elementary properties of probability space, and random variables and their probability distributions. This part also considers the principles of limit theorems, the distribution of random variables, and the so-called student's distribution. The second part explores pertinent topics in mathematical statistics, including the concept of sampling, estimation, and hypotheses testing. This book is intended primarily for undergraduate statistics students.

Autoren/Hrsg.

Lukacs, Eugene

Inhaltsverzeichnis

1;Front Cover;1
2;Probability and Mathematical Statistics: An Introduction;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Introduction;14
7;References;17
8;PART I: PROBABILITY THEORY;18
8.1;Chapter 1. The Probability Space;20
8.1.1;1.1 The Outcome Space;20
8.1.2;1.2 Probabilities;24
8.1.3;1.3 The Axioms;27
8.1.4;1.4 Problems;29
8.1.5;References;31
8.2;Chapter 2. Elementary Properties of Probability Spaces;32
8.2.1;2.1 Simple Consequences of the Axioms;32
8.2.2;2.2 Conditional Probability and Independence;37
8.2.3;2.3 Finite Probability Spaces;44
8.2.4;2.4 Problems;47
8.3;Chapter 3. Random Variables and Their Probability Distributions;50
8.3.1;3.1 Random Variables;50
8.3.2;3.2 Distribution Functions;53
8.3.3;3.3 Examples of Discrete Distributions;57
8.3.4;3.4 Examples of Absolutely Continuous Distributions;61
8.3.5;3.5 Multivariate Distributions;67
8.3.6;3.6 Problems;80
8.3.7;References;82
8.4;Chapter 4. Typical Values;84
8.4.1;4.1 The Mathematical Expectation of a Random Variable;84
8.4.2;4.2 Expectations of Functions of Random Variables;89
8.4.3;4.3 Properties of Expectations;94
8.4.4;4.4 Moments;97
8.4.5;4.5 Regression;109
8.4.6;4.6 Problems;113
8.4.7;Reference;116
8.5;Chapter 5. Limit Theorems;118
8.5.1;5.1 Laws of Large Numbers;118
8.5.2;5.2 The Central Limit Theorem;121
8.5.3;5.3 The Poisson Approximation to the Binomial;126
8.5.4;5.4 Problems;128
8.5.5;References;130
8.6;Chapter 6. Some Important Distributions;132
8.6.1;6.1 The Distribution of the Sum of Independent,Absolutely Continuous Random Variables;132
8.6.2;6.2 Addition of Independent Normal Random Variables;134
8.6.3;6.3 The Chi-Square Distribution;136
8.6.4;6.3 The Chi-Square Distribution;136
8.6.5;6.5 Problems;145
9;PART II: MATHEMATICAL STATISTICS;148
9.1;Chapter 7. Sampling;150
9.1.1;7.1 Statistical Data;150
9.1.2;7.2 Sample Characteristics;152
9.1.3;7.3 Moments and Distributions of Sample Characteristics;155
9.1.4;7.4 Problems;162
9.1.5;References;164
9.2;Chapter 8. Estimation;166
9.2.1;8.1 Properties of Estimates;167
9.2.2;8.2 Point Estimation;170
9.2.3;8.3 Interval Estimation;175
9.2.4;8.4 Problems;182
9.2.5;References;186
9.3;Chapter 9. Testing Hypotheses;188
9.3.1;9.1 Statistical Hypotheses;189
9.3.2;9.2 The Power of a Test;191
9.3.3;9.3 The /-Test;197
9.3.4;9.4 Nonparametric Methods;199
9.3.5;9.5 Problems;204
9.3.6;References;210
10;Appendix A. Some Combinatorial Formulas;212
11;Appendix B.The Gamma Function;218
12;Appendix C. Proof of the Central Limit Theorem;220
13;Appendix D. Tables;232
14;Answers to Selected Problems;240
15;Index;250