Introduction to Probability

INTRODUCTION TO PROBABILITY

Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines

In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite.

This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory.

A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text:

• Includes classroom-tested problems and solutions to probability exercises

• Highlights real-world exercises designed to make clear the concepts presented

• Uses Mathematica software to illustrate the text's computer exercises

• Features applications representing worldwide situations and processes

• Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress

Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.

Autorentext

N. Balakrishnan, PhD, is Distinguished University Professor in the Department of Mathematics and Statistics at McMaster University in Ontario, Canada. He is the author of over twenty books, including Encyclopedia of Statistical Sciences, Second Edition.

Markos V. Koutras, PhD, is Professor in the Department of Statistics and Insurance Science at the University of Piraeus. He is the author/coauthor/editor of 19 books (13 in Greek, 6 in English). His research interests include multivariate analysis, combinatorial distributions, theory of runs/scans/patterns, statistical quality control, and reliability theory.

Konstadinos G. Politis, PhD, is Associate Professor in the Department of Statistics and Insurance Science at the University of Piraeus. He is the author of several articles -published in scientific journals.

Klappentext

Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text:

• Includes classroom-tested problems and solutions to probability exercises
• Highlights real-world exercises designed to make clear the concepts presented
• Uses Mathematica software to illustrate the text's computer exercises
• Features applications representing worldwide situations and processes
• Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.

Zusammenfassung
INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text:

• Includes classroom-tested problems and solutions to probability exercises
• Highlights real-world exercises designed to make clear the concepts presented
• Uses Mathematica software to illustrate the text's computer exercises
• Features applications representing worldwide situations and processes
• Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.

Inhalt
1 Two-dimensional discrete random variables 1

1.1 Introduction 2

1.2 Joint probability function 2

1.3 Marginal distributions 16

1.4 Expectation of a function 25

1.5 Conditional distributions and expectations 33

1.6 Basic concepts and formulas 44

1.7 Computational exercises 45

1.8 Self-assessment exercises 50

1.8.1 True { False Questions 50

1.8.2 Multiple Choice Questions 51

1.9 Review Problems 54

1.10 Applications 59 …