**TEXTBOOK**

**Preface to the Third Edition**

In the second edition of Probability and Statistics, which appeared in 2000, the guiding principle was to make changes in the first edition only where necessary to bring the work in line with the emphasis on topics in contemporary texts. In addition to refinements throughout the text, a chapter on nonparametric statistics was added to extend the applicability of the text without raising its level. This theme is continued in the third edition in which the book has been reformatted and a chapter on Bayesian methods has been added. In recent years, the Bayesian paradigm has come to enjoy increased popularity and impact in such areas as economics, environmental science, medicine, and finance. Since Bayesian statistical analysis is highly computational, it is gaining even wider acceptance with advances in computer technology. We feel that an introduction to the basic principles of Bayesian data analysis is therefore in order and is consistent with Professor Murray R. Spiegel’s main purpose in writing the original text—to present a modern introduction to probability and statistics using a background of calculus. J. SCHILLER R. A. SRINIVASAN

**Preface to the Second Edition**

The first edition of Schaum’s Probability and Statistics by Murray R. Spiegel appeared in 1975, and it has gone through 21 printings since then. Its close cousin, Schaum’s Statistics by the same author, was described as the clearest introduction to statistics in print by Gian-Carlo Rota in his book Indiscrete Thoughts. So it was with a degree of reverence and some caution that we undertook this revision. Our guiding principle was to make changes only where necessary to bring the text in line with the emphasis of topics in contemporary texts. The extensive treatment of sets, standard introductory material in texts of the 1960s and early 1970s, is considerably reduced.

The definition of a continuous random variable is now the standard one, and more emphasis is placed on the cumulative distribution function since it is a more fundamental concept than the probability density function. Also, more emphasis is placed on the P values of hypotheses tests, since technology has made it possible to easily determine these values, which provide more specific information than whether or not tests meet a prespecified level of significance.

Technology has also made it possible to eliminate logarithmic tables. A chapter on nonparametric statistics has been added to extend the applicability of the text without raising its level. Some problem sets have been trimmed, but mostly in cases that called for proofs of theorems for which no hints or help of any kind was given. Overall we believe that the main purpose of the first edition—to present a modern introduction to probability and statistics using a background of calculus—and the features that made the first edition such a great success have been preserved, and we hope that this edition can serve an even broader range of students. J. SCHILLER R. A. SRINIVASAN

**Preface to the First Edition**

The important and fascinating subject of probability began in the seventeenth century through efforts of such mathematicians as Fermat and Pascal to answer questions concerning games of chance. It was not until the twentieth century that a rigorous mathematical theory based on axioms, definitions, and theorems was developed. As time progressed, probability theory found its way into many applications, not only in engineering, science, and mathematics but in fields ranging from actuarial science, agriculture, and business to medicine and psychology. In many instances the applications themselves contributed to the further development of the theory.

The subject of statistics originated much earlier than probability and dealt mainly with the collection, organization, and presentation of data in tables and charts. With the advent of probability it was realized that statistics could be used in drawing valid conclusions and making reasonable decisions on the basis of analysis of data, such as in sampling theory and prediction or forecasting.

The purpose of this book is to present a modern introduction to probability and statistics using a background of calculus. For convenience the book is divided into two parts.

The first deals with probability (and by itself can be used to provide an introduction to the subject), while the second deals with statistics.

The book is designed to be used either as a textbook for a formal course in probability and statistics or as a comprehensive supplement to all current standard texts. It should also be of considerable value as a book of reference for research workers or to those interested in the field for self-study.

The book can be used for a one-year course, or by a judicious choice of topics, a one-semester course. I am grateful to the Literary Executor of the late Sir Ronald A. Fisher, F.R.S., to Dr. Frank Yates, F.R.S., and to Longman Group Ltd., London, for permission to use Table III from their book Statistical Tables for Biological, Agricultural and Medical Research (6th edition, 1974). I also wish to take this opportunity to thank David Beckwith for his outstanding editing and Nicola Monti for his able artwork.