Ebook: Probability for Applications
Author: Paul E. Pfeiffer (auth.)
- Tags: Probability Theory and Stochastic Processes
- Series: Springer Texts in Statistics
- Year: 1990
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
Trials and Events....Pages 3-24
Probability Systems....Pages 25-43
The Sigma Algebra of Events....Pages 44-48
Conditional Probability....Pages 49-71
Independence of Events....Pages 73-87
Conditional Independence of Events....Pages 89-122
Composite Trials....Pages 123-142
Front Matter....Pages 143-143
Random Variables and Probabilities....Pages 145-159
Borel Sets, Random Variables, and Borel Functions....Pages 160-163
Distribution and Density Functions....Pages 165-195
Random Vectors and Joint Distributions....Pages 197-213
Independence of Random Vectors....Pages 215-232
Functions of Random Variables....Pages 233-265
Some Properties of the Quantile Function....Pages 266-271
Front Matter....Pages 273-273
Mathematical Expectation....Pages 275-285
Expectation and Integrals....Pages 287-311
Supplementary Theoretical Details....Pages 312-322
Properties of Expectation....Pages 323-354
Variance and Standard Deviation....Pages 355-370
Covariance, Correlation, and Linear Regression....Pages 371-391
Front Matter....Pages 273-273
Convergence in Probability Theory....Pages 393-408
Transform Methods....Pages 409-441
Front Matter....Pages 443-443
Conditional Expectation, Given a Random Vector....Pages 445-480
Some Theoretical Details....Pages 481-490
Random Selection and Counting Processes....Pages 491-540
Poisson Processes....Pages 541-567
21a....Pages 568-581
Conditional Independence, Given a Random Vector....Pages 583-604
Proofs of Properties....Pages 605-614
Markov Sequences....Pages 615-660
Some Theoretical Details....Pages 661-668
Back Matter....Pages 669-681
Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
Trials and Events....Pages 3-24
Probability Systems....Pages 25-43
The Sigma Algebra of Events....Pages 44-48
Conditional Probability....Pages 49-71
Independence of Events....Pages 73-87
Conditional Independence of Events....Pages 89-122
Composite Trials....Pages 123-142
Front Matter....Pages 143-143
Random Variables and Probabilities....Pages 145-159
Borel Sets, Random Variables, and Borel Functions....Pages 160-163
Distribution and Density Functions....Pages 165-195
Random Vectors and Joint Distributions....Pages 197-213
Independence of Random Vectors....Pages 215-232
Functions of Random Variables....Pages 233-265
Some Properties of the Quantile Function....Pages 266-271
Front Matter....Pages 273-273
Mathematical Expectation....Pages 275-285
Expectation and Integrals....Pages 287-311
Supplementary Theoretical Details....Pages 312-322
Properties of Expectation....Pages 323-354
Variance and Standard Deviation....Pages 355-370
Covariance, Correlation, and Linear Regression....Pages 371-391
Front Matter....Pages 273-273
Convergence in Probability Theory....Pages 393-408
Transform Methods....Pages 409-441
Front Matter....Pages 443-443
Conditional Expectation, Given a Random Vector....Pages 445-480
Some Theoretical Details....Pages 481-490
Random Selection and Counting Processes....Pages 491-540
Poisson Processes....Pages 541-567
21a....Pages 568-581
Conditional Independence, Given a Random Vector....Pages 583-604
Proofs of Properties....Pages 605-614
Markov Sequences....Pages 615-660
Some Theoretical Details....Pages 661-668
Back Matter....Pages 669-681
....