John Schiller - Schaums Outline of Probability and Statistics

Third Edition

Murray R. Spiegel, PhD

Former Professor and Chairman of Mathematics
Rensselaer Polytechnic Institute
Hartford Graduate Center

John J. Schiller, PhD

Associate Professor of Mathematics
Temple University

R. Alu Srinivasan, PhD

Professor of Mathematics
Temple University

Schaums Outline Series

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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. Spiegels main purpose in writing the original textto present a modern introduction to probability and statistics using a background of calculus.

J. SCHILLER
R. A. SRINIVASAN

The first edition of Schaums Probability and Statistics by Murray R. Spiegel appeared in 1975, and it has gone through 21 printings since then. Its close cousin, Schaums 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 nonpara-metric 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 editionto present a modern introduction to probability and statistics using a background of calculusand 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

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.