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Full Description
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.
Contents
I Basic Probability.- 1 Trials and Events.- 2 Probability Systems.- 2a The Sigma Algebra of Events.- 3 Conditional Probability.- 4 Independence of Events.- 5 Conditional Independence of Events.- 6 Composite Trials.- II Random Variables and Distributions.- 7 Random Variables and Probabilities.- 7a Borel Sets, Random Variables, and Borel Functions.- 8 Distribution and Density Functions.- 9 Random Vectors and Joint Distributions.- 10 Independence of Random Vectors.- 11 Functions of Random Variables.- 11a Some Properties of the Quantile Function.- III Mathematical Expectation.- 12 Mathematical Expectation.- 13 Expectation and Integrals.- 13a Supplementary Theoretical Details.- 14 Properties of Expectation.- 15 Variance and Standard Deviation.- 16 Covariance, Correlation, and Linear Regression.- 17 Convergence in Probability Theory.- 18 Transform Methods.- IV Conditional Expectation.- 19 Conditional Expectation, Given a Random Vector.- 19a Some Theoretical Details.- 20 Random Selection and Counting Processes.- 21 Poisson Processes.- 21a.- 22 Conditional Independence, Given a Random Vector.- 22a Proofs of Properties.- 23 Markov Sequences.- 23a Some Theoretical Details.- A Some Mathematical Aids.- B Some Basic Counting Problems.
