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Introduction to Probability SECOND EDITION Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology $14.99   Add to cart

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Introduction to Probability SECOND EDITION Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology

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Introduction to Probability SECOND EDITION Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology WWW site for book information and orders ~ Athena Scientific, Belmont, Massachusetts Athena Scientific Post Office Box 805 Nashua, NH U.S.A. Email: ...

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Introduction to Probability

SECOND EDITION



Dimitri P. Bertsekas and John N. Tsitsiklis

Massachusetts Institute of Technology




WWW site for book information and orders
http://www.athenasc.com




~ Athena Scientific, Belmont, Massachusetts

,Athena Scientific
Post Office Box 805
Nashua, NH 03061-0805
U.S.A.


Email: info@athenasc.com
WWW: http://www.athenasc.com


Cover Design: Ann Gallager



© 2002, 2008 Dimitri P. Bertsekas and John N. Tsitsiklis
All rights reserved. No part of this book may be reproduced in any form by any
electronic or mechanical means (including photocopying, recording, or informa­
tion storage and retrieval) without permission in writing from the publisher .




Publisher's Cataloging-in-Publication Data
Bertsekas, Dimitri P., Tsitsiklis, John N.
Introduction to Probability
Includes bibliographical references and index
L Probabilities. 2. Stochastic Processes. I. Title.
QA273.B475 2008 519.2 - 21
Library of Congress Control Number: 2002092 167

ISBN 978-1-886529-23-6

,To the memory of
Pantelis Bertsekas and Nikos Tsitsiklis

, Preface



Probability is common sense reduced to calculation
Laplace


This book is an outgrowth of our involvement in teaching an introductory prob­
ability course ("Probabilistic Systems Analysis'�) at the Massachusetts Institute
of Technology.
The course is attended by a large number of students with diverse back­
grounds, and a broad range of interests. They span the entire spectrum from
freshmen to beginning graduate students, and from the engineering school to the
school of management. Accordingly, we have tried to strike a balance between
simplicity in exposition and sophistication in analytical reasoning. Our key aim
has been to develop the ability to construct and analyze probabilistic models in
a manner that combines intuitive understanding and mathematical precision.
In this spirit, some of the more mathematically rigorous analysis has been
just sketched or intuitively explained in the text. so that complex proofs do not
stand in the way of an otherwise simple exposition. At the same time, some of
this analysis is developed (at the level of advanced calculus) in theoretical prob­
lems, that are included at the end of the corresponding chapter. FUrthermore,
some of the subtler mathematical issues are hinted at in footnotes addressed to
the more attentive reader.
The book covers the fundamentals of probability theory (probabilistic mod­
els, discrete and continuous random variables, multiple random variables, and
limit theorems) , which are typically part of a first course on the subject. It
also contains, in Chapters 4-6 a number of more advanced topics, from which an
instructor can choose to match the goals of a particular course. In particular, in
Chapter 4, we develop transforms, a more advanced view of conditioning, sums
of random variables, least squares estimation, and the bivariate normal distribu-

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