An Introduction to Probability and Statistics

PREFACE TO THE THIRD EDITION xiii
 
PREFACE TO THE SECOND EDITION xv
 
PREFACE TO THE FIRST EDITION xvii
 
ACKNOWLEDGMENTS xix
 
ENUMERATION OF THEOREMS AND REFERENCES xxi
 
1 Probability 1
 
1.1 Introduction 1
 
1.2 Sample Space 2
 
1.3 Probability Axioms 7
 
1.4 Combinatorics: Probability on Finite Sample Spaces 20
 
1.5 Conditional Probability and Bayes Theorem 26
 
1.6 Independence of Events 31
 
2 Random Variables and Their Probability Distributions 39
 
2.1 Introduction 39
 
2.2 Random Variables 39
 
2.3 Probability Distribution of a Random Variable 42
 
2.4 Discrete and Continuous Random Variables 47
 
2.5 Functions of a Random Variable 55
 
3 Moments and Generating Functions 67
 
3.1 Introduction 67
 
3.2 Moments of a Distribution Function 67
 
3.3 Generating Functions 83
 
3.4 Some Moment Inequalities 93
 
4 Multiple Random Variables 99
 
4.1 Introduction 99
 
4.2 Multiple Random Variables 99
 
4.3 Independent Random Variables 114
 
4.4 Functions of Several Random Variables 123
 
4.5 Covariance, Correlation and Moments 143
 
4.6 Conditional Expectation 157
 
4.7 Order Statistics and Their Distributions 164
 
5 Some Special Distributions 173
 
5.1 Introduction 173
 
5.2 Some Discrete Distributions 173
 
5.2.1 Degenerate Distribution 173
 
5.2.2 Two-Point Distribution 174
 
5.2.3 Uniform Distribution on n Points 175
 
5.2.4 Binomial Distribution 176
 
5.2.5 Negative Binomial Distribution (Pascal or Waiting Time Distribution) 178
 
5.2.6 Hypergeometric Distribution 183
 
5.2.7 Negative Hypergeometric Distribution 185
 
5.2.8 Poisson Distribution 186
 
5.2.9 Multinomial Distribution 189
 
5.2.10 Multivariate Hypergeometric Distribution 192
 
5.2.11

Vijay K. Rohatgi, PhD, is Professor Emeritus in the Department of Mathematics and Statistics at Bowling Green State University. An Investment Research Consultant for PRI Investments, he is also the author of several books and over 100 research papers.
 
A. K. Md. Ehsanes Saleh, PhD, is Distinguished Research Professor in the School of Mathematics and Statistics at Carleton University. Dr. Saleh is the author of more than 200 journal articles, and his research interests include nonparametric statistics, order statistics, and robust estimation.