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Probability 概率论

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Probability 概率论

最 低 价:¥72.80

定 价:¥80.91

作 者:C. R. Heathcote 著

出 版 社:Oversea Publishing House

出版时间:2000-4-1

I S B N:9780486411491

  • Probability 概率论
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    72.80元

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    内容简介

    This volume will serve as an excellent introduction to mathematical statistics and probability for students who have completed a course in calculus and real variables. Prerequisites include some knowledge of set theory and Riemann integration, and familiarity with the elementary operations of analysis.
    Method and basic theory receive equal emphasis, starting with the fundamental notions of probability spaces, random variables, distrib-ution functions, and generating functions. Other topics include joint distributions and the convergence properties of sequences of random variables, plus an explanation of almost sure convergence for readers not acq ainted with measure theory.
    A substantial number of worked examples are provided in the text, in addition to over 250 exercises. Starred sections treat special or more difficult topics and could be omitted from a short introductory course.
    Intended to provide a suitable preparation for further study of statis- tics and probability, this volume will also interest mathematically inclined general readers.

    作者简介

    目录

    Preface
    Principal notations
    1 PROBABILITY SPACES AND RANDOM VARIABLES
    1.1 Probability spaces
    1.2 Properties of probability spaces
    1.3 Finite probability spaces
    1.4 Random variables
    1.5 Expectation and moments
    Appendix Monotone sequences of events
    2 SOME REAL VARIABLE THEORY
    2.1 Taylor's Theorem
    2.2 Power series and probability generating functions
    2.3 Integral transforms
    2.4 Transformations
    2.5 Special functions Table of generating functions
    3 SEVERAL RANDOM VARIABLES
    3.1 Joint distributions
    3.2 Conditional probability
    3.3 Independent random variables
    3.4 Bayes's Theorem
    3.5 Sequences of dependent random variables;Markov chains
    4 WEAK CONVERGENCE
    4.1 Sequences of distribution functions
    4.2 The weak law of large numbers
    4.3 The central limit theorem
    4.4 Distributions derived from the normal
    4.5 Some limit theorems for Markov chains
    5 ALMOST SURE CONVERGENCE
    5.1 Infinite sequences of events
    5.2 Almost sure convergence
    5.3 The strong law of large numbers
    5.4 The strong law (continued)
    5.5 Occupation times and recurrent Markov chains
    Answers to selected exercises
    Index

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