Book 2004

Probability Essentials

Authors:

ISBN: 978-3-540-43871-7 (Print) 978-3-642-55682-1 (Online)

Table of contents (28 chapters)

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  1. Front Matter

    Pages I-X

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    Chapter

    Pages 1-5

    Introduction

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    Chapter

    Pages 7-13

    Axioms of Probability

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    Chapter

    Pages 15-20

    Conditional Probability and Independence

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    Chapter

    Pages 21-26

    Probabilities on a Finite or Countable Space

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    Chapter

    Pages 27-34

    Random Variables on a Countable Space

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    Chapter

    Pages 35-38

    Construction of a Probability Measure

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    Chapter

    Pages 39-46

    Construction of a Probability Measure on R

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    Chapter

    Pages 47-50

    Random Variables

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    Chapter

    Pages 51-64

    Integration with Respect to a Probability Measure

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    Chapter

    Pages 65-75

    Independent Random Variables

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    Chapter

    Pages 77-85

    Probability Distributions on R

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    Chapter

    Pages 87-101

    Probability Distributions on R n

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    Chapter

    Pages 103-109

    Characteristic Functions

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    Chapter

    Pages 111-116

    Properties of Characteristic Functions

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    Chapter

    Pages 117-123

    Sums of Independent Random Variables

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    Chapter

    Pages 125-139

    Gaussian Random Variables (The Normal and the Multivariate Normal Distributions)

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    Chapter

    Pages 141-149

    Convergence of Random Variables

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    Chapter

    Pages 151-166

    Weak Convergence

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    Chapter

    Pages 167-171

    Weak Convergence and Characteristic Functions

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    Chapter

    Pages 173-179

    The Laws of Large Numbers

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