Fundamentals of Probability: A First Course
This is a text encompassing all of the standard topics in introductory probability theory, together with a significant amount of optional material of emerging importance. The emphasis is on a lucid and accessible writing style, mixed with a large number o
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Anirban DasGupta
Fundamentals of Probability: A First Course
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Anirban DasGupta Purdue University Dept. Statistics & Mathematics 150 N. University Street West Lafayette IN 47907 USA [email protected]
Editorial Board George Casella Department of Statistics University of Florida Gainesville, FL 32611-8545 USA
Stephen Fienberg Department of Statistics Carnegie Mellon University Pittsburgh, PA 15213-3890 USA
Ingram Okin Department of Statistics Stanford University Stanford, CA 94305 USA
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ISSN 1431-875X ISBN 978-1-4419-5779-5 e-ISBN 978-1-4419-5780-1 DOI 10.1007/978-1-4419-5780-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010924739 c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To the Memory of William Feller, whose books inspired my love of probability, and to Dev Basu, the greatest teacher I have known
Preface
Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the external world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-first century, as difficult new problems emerge, that will require more sophisticated models and analysis. This is a text on the fundamentals of the theory of probability at an undergraduate or first-year graduate level for students in science, engineering, and economics. The only mathematical background required is knowledge of univariate and multivariate calculus and basic linear algebra. The book covers all of the standard topics in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random var
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