Fundamentals of Probability and Statistics for Engineers

Introduction

This book was written for an introductory one-semester or two-quarter course in probability and statistics for students in engineering and applied sciences. N o previous knowledge of probability or statistics is presumed but a good understanding of calculus is a prerequisite for the material.

The development of this book was guided by a number of considerations observed over many years of teaching courses in this subject area, including the following: 

1. As an introductory course, a sound and rigorous treatment of the basic principles is imperative for a proper understanding of the subject matter and for confidence in applying these principles to practical problem solving. A student, depending upon his or her major field of study, will no doubt pursue advanced work in this area in one or more of the many possible directions. H ow well is he or she prepared to do this strongly depends on his or her mastery of the fundamentals.
2. It is important that the student develop an early appreciation for applications. Demonstrations of the utility of this material in Non superficial applications not only sustain student interest but also provide the student with stimulation to delve more deeply into the fundamentals.
3. Most of the students in engineering and applied sciences can only devote one semester or two quarters to a course of this nature in their programs. Recognizing that the coverage is time limited, it is important that the material be self-contained, representing a reasonably complete and applicable body of knowledge.

The choice of the contents for this book is in line with the foregoing observations. The major objective is to give a careful presentation of the fundamentals in probability and statistics, the concept of probabilistic modeling, and the process of model selection, verification, and analysis. In this text, definitions and theorems are carefully stated and topics rigorously treated but care is taken not to become entangled in excessive mathematical details.

Practical examples are emphasized; they are purposely selected from many different fields and not slanted toward any particular applied area. The same objective is observed in making up the exercises at the back of each chapter. Because of the self-imposed criterion of writing a comprehensive text and presenting it within a limited time frame, there is a tight continuity from one topic to the next.

Some flexibility exists in Chapters 6 and 7 that include discussions on more specialized distributions used in practice. F or example, extreme-value distributions may be bypassed, if it is deemed necessary, without serious loss of continuity.

Also, Chapter 11 on linear models may be deferred to a follow-up course if time does not allow its full coverage. It is a pleasure to acknowledge the substantial help I received from students in my courses over many years and from my colleagues and friends.

Their constructive comments on preliminary versions of this book led to many improvements. My sincere thanks go to M rs. Carmella Gosden, who efficiently typed several drafts of this book. As in all my undertakings, my wife, Dottie, cared about this project and gave me her loving support for which I am deeply grateful