概率統(tǒng)計(jì)高級(jí)教程卷1

內(nèi)容概要

　　This is an update Text book for beginning graduate students in Mathematics， Probability and Statistics， Engineering， Computer Sciences， Mathematical Economics. It distinguishes from all existing texts on the subject from its pedagogical spirit， namely， motivations before mathematics： mathematics tools are only introduced when needed and motivated. All theoretical results are proved in a friendly fashion. Teaching the students， not only the concepts and possible applications，but also guiding the students with proof techniques. This series will help students to learn with full understanding and appreciation of the subject. It will provide interested students with solid background for research.

作者簡(jiǎn)介

作者：(美國(guó))HUNG T .NGUYEN TONGHUI WANG

書籍目錄

Preface1 Models for Random Experiments1.1 Games of Chance1.2 Experiments with Infinitely Many Outcomes1.3 Structure and Properties of Probability Spaces1.4 Conditioning and Independence1.5 Exercises2 Models for Laws of Random Phenomena2.1 Discrete Sample Spaces2.2 The Sample Space R2.3 The Sample Space Rd2.4 The Sample Space of Closed Sets of Rd2.5 Exercises3 Models for Populations3.1 Random Elements3.2 Distributions of Random Elements3.3 Some Descriptive Quantities of Random Variables/Integration3.3.1 The concept of expectation of random variables3.3.2 Properties of expectation3.3.3 Computations of expectation3.3.4 The Choquet integral and random sets3.4 Independence and Conditional Distributions3.5 Exercises4 Some Distribution Theory4.1 The Method of Transformations4.2 The Method cf Convolution4.3 Generating Functions4.4 Characteristic Functions4.5 Exercites5 Convergence Concepts5.1 Convergence cf Random Elements5.2 Convergence cf Moments5.3 Convergence of Distributions5.4 Convergence cf Probability Measures5.5 Exercises6 Some Limit Theorems For Large Sample Statistics6.1 Laws of Large Numbers6.1.1 Independent random variables6.1.2 Independent and identically distributed random variables6.1.3 Some examples6.1.4 Uniform laws of large numbers*6.2 Central Limit Theorem6.2.1 Independent and identically distributed random variables6.2.2 Independent random variables6.3 Large deviations*6.3.1 Some motivations6.3.2 Formulation of large deviations principles6.3.3 Large deviations techniques6.4 Exercises7 Conditional Expectation and Martingales7.1 The Discrete Case7.2 The General Case7.3 Properties of Conditional Expectation7.4 Martingales7.5 ExercisesBibliographyIndex

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