Introduction to Probability (Springer Texts in Electrical Engineering)

This book was written for an introductory one-term course in probability. It is intended to provide the minimum background in probability that is necessary for students interested in applications to engineering and the sciences. Although it is aimed primarily at upperclassmen and beginning graduate students, the only prere­ quisite is the standard calculus course usually required of under­ graduates in engineering and science. Most beginning students will have some intuitive notions of the meaning of probability based on experiences involving, for example, games of chance. This book develops from these notions a set of precise and ordered concepts comprising the elementary theory of probability. An attempt has been made to state theorems carefully, but the level of the proofs varies greatly from formal arguments to appeals to intuition. The book is in no way intended as a substi­ tu te for a rigorous mathematical treatment of probability. How­ ever, some small amount of the language of formal mathematics is used, so that the student may become better prepared (at least psychologically) either for more formal courses or for study of the literature. Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided. Instructors who adopt the text for classroom use may obtain a Solutions Manual for all of the problems by writing to the author. Front Matter....Pages i-x Introduction and Preliminary Concepts....Pages 1-29 Random Variables....Pages 30-43 Distribution and Density Functions....Pages 44-78 Expectations and Characteristic Functions....Pages 79-113 The Binomial, Poisson, and Normal Distributions....Pages 114-134 The Multivariate Normal Distribution....Pages 135-151 The Transformation of Random Variables....Pages 152-183 Sequences of Random Variables....Pages 184-215 Back Matter....Pages 216-249