Page 20 - Fundamentals of Probability and Statistics for Engineers

Introduction 3

may be rejected at this stage as a result of inadequate inductive reasoning or
insufficient or deficient data. A reexamination of factual observations or add-
itional data may be required here. Finally, model analysis and deduction are
made to yield desired answers upon model substantiation.
In line with this outline of the basic steps, the book is divided into two parts.
Part A (Chapters 2–7) addresses probability fundamentals involved in steps
A ! C, B ! C, and E ! F (Figure 1.1). Chapters 2–5 provide these funda-
mentals, which constitute the foundation of all subsequent development. Some
important probability distributions are introduced in Chapters 6 and 7. The
nature and applications of these distributions are discussed. An understanding
of the situations in which these distributions arise enables us to choose an
appropriate distribution, or model, for a scientific phenomenon.
Part B (Chapters 8–11) is concerned principally with step D ! E (Figure 1.1),
the statistical inference portion of the text. Starting with data and data repre-
sentation in Chapter 8, parameter estimation techniques are carefully developed
in Chapter 9, followed by a detailed discussion in Chapter 10 of a number of
selected statistical tests that are useful for the purpose of model verification. In
Chapter 11, the tools developed in Chapters 9 and 10 for parameter estimation
and model verification are applied to the study of linear regression models, a very
useful class of models encountered in science and engineering.
The topics covered in Part B are somewhat selective, but much of the
foundation in statistical inference is laid. This foundation should help the
reader to pursue further studies in related and more advanced areas.

1.2 PROBABILITY TABLES AND COMPUTER SOFTWARE

The application of the materials in this book to practical problems will require
calculations of various probabilities and statistical functions, which can be time
consuming. To facilitate these calculations, some of the probability tables are
provided in Appendix A. It should be pointed out, however, that a large
number of computer software packages and spreadsheets are now available
that provide this information as well as perform a host of other statistical
calculations. As an example, some statistical functions available in Microsoft Õ
Excel TM 2000 are listed in Appendix B.

1.3 PREREQUISITES

The material presented in this book is calculus-based. The mathematical pre-
requisite for a course using this book is a good understanding of differential
and integral calculus, including partial differentiation and multidimensional
integrals. Familiarity in linear algebra, vectors, and matrices is also required.

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