共找到 4 项 “Sheldon Ross著” 相关结果
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出版社:机械工业出版社,2006
简介: 本书是一本概率论的入门教材,系统介绍了概率论的基础理论及应用,在取材、结构和写作方法等方面具有鲜明的特点。通过例题阐述概率论的基本概念与方法是本书的一大特色。作者独具匠心地选择和编排了大量例题与习题,这些内容约占全书的三分之二。通过这些例题和习题,读者可以了解概率论在各个领域的广泛应用,如基因、彩票、法庭判决、NBA选秀等。 本书系统介绍了概率论的基础理论及应用,主要内容包括组合分析、概率论和公理、条件概率与独立性、随机变量及其分布、数学期望、极限定理、、随机模拟等。另外,作者精心选择了大量的例题和习题,提示了概率论在各个领域的广泛应用。 本书通俗易懂,可作为高等院校相关专业概论课程的教材或教学参考书。
A first course in probability = 概率论基础教程 / 第7版.
作者: Sheldon Ross著.
简介: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 APPENDICES A Answers to Selected Problems B Solutions to Self-Test Problems and Exercises Index