Probability for Applications

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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
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