Seymour Lipschutz - Schaums Outline of Probability

SEYMOUR LIPSCHUTZ, who is presently on the mathematics faculty at Temple University, formerly taught at the Polytechnic Institute of Brooklyn and was visiting professor in the Computer Science Department of Brooklyn College. He received his Ph.D. in 1960 at the Courant Institute of Mathematical Sciences of New York University. Some of his other books in the Schaums Outline Series are Beginning Linear Algebra, Discrete Mathematics, and Linear Algebra. MARC LARS LIPSON is on the faculty at the University of Virginia and formerly taught at Northeastern University, Boston University, and the University of Georgia. in finance in 1994 from the University of Michigan. in finance in 1994 from the University of Michigan.

He is also coauthor of Schaums Outline of Discrete Mathematics with Seymour Lipschutz. Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-0-07-181658-8
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Probability theory had its beginnings in the early seventeenth century as a result of investigations of various games of chance. Since then many leading mathematicians and scientists made contributions to this theory. However, despite its long and active history, probability theory was not axiomatized until the twentieth century. This axiomatic development, called modern probability theory, was then able to make the concepts of probability precise and place them on a firm mathematical foundation.

This book is designed for an introductory course in probability with high school algebra as the main prerequisite. It can serve as a text for such a course, or as a supplement to all current comparable texts. The book should also prove to be useful as a supplement to texts and courses in statistics. Furthermore, as the book is complete and self-contained it can easily be used for self-study. This new edition includes and expands the content of the first edition. It begins with a chapter on sets and their operations, and then with a chapter on techniques of counting.

Next comes a chapter on probability spaces, and then a chapter on conditional probability and independence. The fifth and main chapter is on random variables where we define expectation, variance, and standard deviation, and prove Chebyshevs inequality and the law of large numbers. Although calculus is not a prerequisite, both discrete and continuous random variables are considered. We follow with a separate chapter on specific distributions, mainly the binomial, normal, and Poisson distributions. Here the central limit theorem is given in the context of the normal approximation to the binomial distribution. The seventh and last chapter offers a thorough elementary treatment of Markov chains with applications.

This new edition also has two new appendixes. The first is on descriptive statistics where expectation, variance, and standard deviation are again defined, but now in the context of statistics. This appendix also treats bivariate data, including scatterplots, the correlation coefficient, and methods of least squares. The second appendix discusses the chi-square distribution and various applications in the context of testing hypotheses. These two new appendixes motivate many of the concepts which appear in the chapters on probability, and also make the book even more useful as a supplement to texts and courses in statistics. The positive qualities that distinguished the first edition have been retained.

Each chapter begins with clear statements of pertinent definitions, principles, and theorems together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems. The solved problems serve to illustrate and amplify the theory, and provide the repetition of basic principles so vital to effective learning. Proof of most of the theorems is included among the solved problems. The supplementary problems serve as a complete review of the material of each chapter. Finally, we wish to thank the staff of McGraw-Hill, especially Barbara Gilson and Maureen Walker, for their excellent cooperation.

SEYMOUR LIPSCHUTZ
Temple University MARC LARS LIPSON

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