Ebook: Probability

This book is a text at the introductory graduate level, for use in the one­ semester or two-quarter probability course for first-year graduate students that seems ubiquitous in departments of statistics, biostatistics, mathemat­ ical sciences, applied mathematics and mathematics. While it is accessi­ ble to advanced ("mathematically mature") undergraduates, it could also serve, with supplementation, for a course on measure-theoretic probability. Students who master this text should be able to read the "hard" books on probability with relative ease, and to proceed to further study in statistics or stochastic processes. This is a book to teach from. It is not encyclopredic, and may not be suitable for all reference purposes. Pascal once apologized to a correspondent for having written a long letter, saying that he hadn't the time to write a short one. I have tried to write a short book, which is quite deliberately incomplete, globally and locally. Many topics, including at least one of everyone's favorites, are omitted, among them, infinite divisibility, interchangeability, large devia­ tions, ergodic theory and the Markov property. These can be supplied at the discretion and taste of instructors and students, or to suit particular interests.

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This is a textbook which will provide students with a straightforward introduction to the mathematical theory of probability. It is written with the aim of presenting the central results and techniques of the subject in a complete and self-contained account. As a result, the emphasis is on giving results in simple forms with clear proofs and to eschew more powerful forms of theorems which require technically involved proofs. Any graduate student who has a familiarity with real analysis will be able to use this text - measure theory is used only where necessary and undue abstraction is avoided. Throughout there are a wide variety of exercises to illustrate and to develop ideas in the text.

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This is a textbook which will provide students with a straightforward introduction to the mathematical theory of probability. It is written with the aim of presenting the central results and techniques of the subject in a complete and self-contained account. As a result, the emphasis is on giving results in simple forms with clear proofs and to eschew more powerful forms of theorems which require technically involved proofs. Any graduate student who has a familiarity with real analysis will be able to use this text - measure theory is used only where necessary and undue abstraction is avoided. Throughout there are a wide variety of exercises to illustrate and to develop ideas in the text.
Content:
Front Matter....Pages i-xxi
Prelude: Random Walks....Pages 1-14
Probability....Pages 15-42
Random Variables....Pages 43-70
Independence....Pages 71-100
Expectation....Pages 101-134
Convergence of Random Variables....Pages 135-162
Characteristic Functions....Pages 163-182
Classical Limit Theorems....Pages 183-216
Prediction and Conditional Expectation....Pages 217-242
Martingales....Pages 243-270
Back Matter....Pages 271-283

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This is a textbook which will provide students with a straightforward introduction to the mathematical theory of probability. It is written with the aim of presenting the central results and techniques of the subject in a complete and self-contained account. As a result, the emphasis is on giving results in simple forms with clear proofs and to eschew more powerful forms of theorems which require technically involved proofs. Any graduate student who has a familiarity with real analysis will be able to use this text - measure theory is used only where necessary and undue abstraction is avoided. Throughout there are a wide variety of exercises to illustrate and to develop ideas in the text.
Content:
Front Matter....Pages i-xxi
Prelude: Random Walks....Pages 1-14
Probability....Pages 15-42
Random Variables....Pages 43-70
Independence....Pages 71-100
Expectation....Pages 101-134
Convergence of Random Variables....Pages 135-162
Characteristic Functions....Pages 163-182
Classical Limit Theorems....Pages 183-216
Prediction and Conditional Expectation....Pages 217-242
Martingales....Pages 243-270
Back Matter....Pages 271-283
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