概率論基礎(chǔ)教程

內(nèi)容概要

本書是全球高校廣泛采用的概率論教材，通過大量的例子講述了概率論的基礎(chǔ)知識，主要內(nèi)容有組合分析、概率論公理化、條件概率和獨立性、離散和連續(xù)型隨機變量、隨機變量的聯(lián)合分布、期望的性質(zhì)、極限定理等。本書附有大量的練習(xí)，分為習(xí)題、理論習(xí)題和自檢習(xí)題三大類，其中自檢習(xí)題部分還給出全部解答?！　”緯鳛楦怕收摰娜腴T書，適用于大專院校數(shù)學(xué)、統(tǒng)計、工程和相關(guān)專業(yè)(包括計算科學(xué)、生物、社會科學(xué)和管理科學(xué))的學(xué)生閱讀，也可供概率應(yīng)用工作者參考。

作者簡介

Sheldon M.Ross，國際知名概率與統(tǒng)計學(xué)家，南加州大學(xué)工業(yè)工程與運籌系系主任。畢業(yè)于斯坦福大學(xué)統(tǒng)計系，曾在加州大學(xué)伯克利分校任教多年。研究領(lǐng)域包括：隨機模型、仿真模擬、統(tǒng)計分析、金融數(shù)學(xué)等。Ross教授著述頗豐，他的多種暢銷數(shù)學(xué)和統(tǒng)計教材均產(chǎn)生了世界性的影響，如S

書籍目錄

1　Combinatorial Analysis　　1.1　Introduction　　1.2　The Basic Principle of Counting　　1.3　Permutations　　1.4　Combinations　　1.5　Multinomial Coefficients　　1.6　The Number of Integer Solutions of Equations*　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　2　Axioms of Probability　　2.1　Introduction　　2.2　Sample Space and Events　　2.3　Axioms of Probability　　2.4　Some Simple Propositions　　2.5　Sample Spaces Having Equally Likely Outcomes　　2.6　Probability as a Continuous Set Function*　　2.7　Probability as a Measure of Belief　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　3　Conditional Probability and Independence　　3.1　Introduction　　3.2　Conditional Probabilities　　3.3　Bayes' Formula　　3.4　Independent Events　　3.5　P(.|F) Is a Probability　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　4　Random Variables　　4.1　Random Variables　　4.2　Discrete Random Variables　　4.3　Expected Value　　4.4　Expectation of a Function of a Random Variable　　4.5　Variance　　4.6　The Bernoulli and Binomial Random Variables　　　4.6.1　Properties of Binomial Random Variables　　　4.6.2　Computing the Binomial Distribution Function　　4.7 The　Poisson Random Variable　　　4.7.1　Computing the Poisson Distribution Function　　4.8　Other Discrete Probability Distributions　　　4.8.1　The Geometric Random Variable　　　4.8.2　The Negative Binomial Random Variable　　　4.8.3　The Hypergeometric Random Variable　　　4.8.4　The Zeta (or Zipf) Distribution　　4.9　Properties of the Cumulative Distribution Function　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　5　Continuous Random Variables　　5.1　Introduction　　5.2　Expectation and Variance of Continuous Random Variables　　5.3　The Uniform Random Variable　　5.4　Normal Random Variables　　　5.4.1　The Normal Approximation to the Binomial Distribution　　5.5　Exponential Random Variables　　　5.5.1　Hazard Rate Functions　　5.6　Other Continuous Distributions　　　5.6.1　The Gamma Distribution　　　5.6.2　The Weibull Distribution　　　5.6.3　The Cauchy Distribution　　　5.6.4　The Beta Distribution　　5.7　The Distribution of a Function of a Random Variable　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　6　Jointly Distributed Random Variables　　6.1　Joint Distribution Functions　　6.2　Independent Random Variables　　6.3　Sums of Independent Random Variables　　6.4　Conditional Distributions: Discrete Case　　6.5　Conditional Distributions: Continuous Case　　6.6　Order Statistics*　　6.7　Joint Probability Distribution of Functions of Random Variables　　6.8　Exchangeable Random Variables*　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　7　Properties of Expectation　　7.1　Introduction　　7.2　Expectation of Sums of Random Variables　　　7.2.1　Obtaining Bounds from Expectations via the Probabilistic Method*　　　7.2.2　The Maximum-Minimums Identity*　　7.3　Moments of the Number of Events that Occur　　7.4　Covariance, Variance of Sums, and Correlations　　7.5　Conditional Expectation　　　7.5.1　Definitions　　　7.5.2　Computing Expectations by Conditioning　　　7.5.3　Computing Probabilities by Conditioning　　　7.5.4　Conditional Variance　　7.6　Conditional Expectation and Prediction　　7.7　Moment Generating Functions　　　7.7.1　Joint Moment Generating Functions　　7.8　Additional Properties of Normal Random Variables　　　7.8.1　The Multivariate Normal Distribution　　　7.8.2　The Joint Distribution of the Sample Mean and Sample Variance　　7.9　General Definition of Expectation　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　8　Limit Theorems　　8.1　Introduction　　8.2　Chebyshev's Inequality and the Weak Law of Large Numbers　　8.3　The Central Limit Theorem　　8.4　The Strong Law of Large Numbers　　8.5　Other Inequalities　　8.6　Bounding The Error Probability　　　Summary　　　Problems　　　Theoretical Exercises　　　Self-Test Problems and Exercises　9　Additional Topics in Probability　　9.1　The Poisson Process　　9.2　Markov Chains　　9.3　Surprise, Uncertainty, and Entropy　　9.4　Coding Theory and Entropy　　　Summary　　　Theoretical Exercises　　　Self-Test Problems and Exercises　10　Simulation　　10.1　Introduction　　10.2　General Techniques for Simulating Continuous Random Variables　　　10.2.1　The Inverse Transformation Method　　　10.2.2　The Rejection Method　　10.3　Simulating from Discrete Distributions　　10.4　Variance Reduction Techniques　　　10.4.1　Use of Antithetic Variables　　　10.4.2　Variance Reduction by Conditioning　　　10.4.3　Control Variates　　　Summary　　　Problems　　　Self-Test Problems and Exercises　APPENDICESA　Answers to Selected Problems　B　Solutions to Self-Test Problems and Exercises　Index　

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