# Probability for Applications

Springer Science & Business Media, Dec 6, 2012 - Mathematics - 679 pages
Objecti'ves. As the title suggests, this book provides an introduction to probability designed to prepare the reader for intelligent and resourceful applications in a variety of fields. Its goal is to provide a careful exposition of those concepts, interpretations, and analytical techniques needed for the study of such topics as statistics, introductory random processes, statis tical communications and control, operations research, or various topics in the behavioral and social sciences. Also, the treatment should provide a background for more advanced study of mathematical probability or math ematical statistics. The level of preparation assumed is indicated by the fact that the book grew out of a first course in probability, taken at the junior or senior level by students in a variety of fields-mathematical sciences, engineer ing, physics, statistics, operations research, computer science, economics, and various other areas of the social and behavioral sciences. Students are expected to have a working knowledge of single-variable calculus, including some acquaintance with power series. Generally, they are expected to have the experience and mathematical maturity to enable them to learn new concepts and to follow and to carry out sound mathematical arguments. While some experience with multiple integrals is helpful, the essential ideas can be introduced or reviewed rather quickly at points where needed.

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### Contents

 Trials and Events 3 Probability Systems 25 2a The Sigma Algebra of Events 44 Independence of Events 73 Conditional Independence of Events 89 88 Composite Trials 123 Random Variables and Probabilities 145 7a Borel Sets Random Variables and Borel Functions 160
 Variance and Standard Deviation 355 Covariance Correlation and Linear Regression 371 Convergence in Probability Theory 393 392 Transform Methods 409 Conditional Expectation 443 19a Some Theoretical Details 481 Random Selection and Counting Processes 491 Poisson Processes 541

 Random Vectors and Joint Distributions 197 Independence of Random Vectors 215 214 Functions of Random Variables 233 11a Some Properties of the Quantile Function 266 Mathematical Expectation 273 Expectation and Integrals 287 13a Supplementary Theoretical Details 312 Properties of Expectation 323
 21a 568 Conditional Independence Given a Random Vector 583 22a Proofs of Properties 605 Markov Sequences 615 23a Some Theoretical Details 661 A Some Mathematical Aids 669 Index 675 Copyright