魏军强、郑宏文编著的《工科概率统计》的主要内容包括:概率论的基本概念、随机变量及其分布、随机变量的数字特征、大数定律和中心极限定理、描述性统计、数理统计的基本概念、参数的点估计与区间估计、参数的假设检验等。
本书偏重于工科各专业与概率统计思想、方法的联系,可作为工科、理科非数学专业及经济管理类等专业本科生和留学生的概率论与数理统计教材,同时也可供相关科技人员参考。
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书名 | 工科概率统计(英文版普通高等教育规划教材) |
分类 | 科学技术-自然科学-数学 |
作者 | 魏军强//郑宏文 |
出版社 | 北京交通大学出版社 |
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简介 | 内容推荐 魏军强、郑宏文编著的《工科概率统计》的主要内容包括:概率论的基本概念、随机变量及其分布、随机变量的数字特征、大数定律和中心极限定理、描述性统计、数理统计的基本概念、参数的点估计与区间估计、参数的假设检验等。 本书偏重于工科各专业与概率统计思想、方法的联系,可作为工科、理科非数学专业及经济管理类等专业本科生和留学生的概率论与数理统计教材,同时也可供相关科技人员参考。 目录 Chapter 1 Probability and Its Properties 1.1 Basic Probability Concepts 1.2 Axioms and Properties of Probability 1.2.1 Axioms Definition of Probability 1.2.2 Properties of Probability 1.3 Classical Probability and Counting Techniques 1.3.1 Counting Principles 1.3.2 Classical Probability 1.4 Conditional Probability, Independence of Two and Several Events 1.4.1 Conditional Probability 1.4.2 Independence 1.5 Law of Total Probability and Bayes' Theorem Exercises Chapter 2 Random Variables and Their Distributions 2.1 Random Variables 2.2 Distribution of a Random Variable and Distribution Function 2.3 Classical Discrete Random Variables and Continuous Random Variables 2.3.1 Discrete Distribution 2.3.2 Continuous Distribution 2.4 Distribution of Functions of a Random Variable Exercises Chapter 3 Random Vectors and Their Distributions 3.1 Jointly Distributed Random Variables 3.2 Marginal Distribution and Conditional Distribution of Two Random Variables 3.3 Independent Random Variables 3.4 Distribution of Functions of Two Random Variables Exercises Chapter4 Expectations and Moments 4.1 Mathematical Expectation and Its Properties 4.1.1 Mathematical Expectation 4.1.2 Properties of the Expectation 4.2 Variance and Its Properties 4.2.1 Definition of the Variance 4.2.2 Properties of the Variance 4.3 Expectations and Variances of Special Probability Distributions 4.3.1 Case for Common Discrete Random Variables 4.3.2 Case for Common Continuous Random Variables 4.4 Moments 4.4.1 Covariance and Correlation Coefficients 4.4.2 Moments Exercises Chapter 5 The Law of Large Numbers and the Central Limit Theorem 5. I The Law of Large Numbers and Its Applications 5.1.1 Chebyshev's Inequality 5.1.2 The Law of Large Numbers 5.2 The Central Limit Theorem and Its Applications Exercises Chapter 6 Basic Conceptions of Statistics 6.1 Basic Conceptions of Sampling 6.2 Descriptive Statistics 6.2.1 Summarizing Data--Numerical Methods 6.2.2 Summarizing Data--Graphical Methods 6.3 Fundamental Sampling Distributions 6.3.1 The Chi-squared Distribution 6.3.2 The t-Distribution 6.3.3 The F-Distribution 6.4 Sampling Distribution Theorems Exercises Chapter 7 Parameter Estimation 7.1 General Concepts of Point Estimation 7.2 Methods of Point Estimation 7.2.1 Method of Moments 7.2.2 Method of Maximum Likelihood Estimation 7.3 Criteria for Good Estimators 7.4 Interval Estimation 7.4.1 Confidence Intervals Based on a Single Sample 7.4.2 Confidence Intervals Based on Two Samples 7.5 One-sided Confidence Intervals (Confidence Bounds) Exercises Chapter 8 Hypothesis Testing 8.1 Hypotheses and Testing Procedures 8.1.1 Hypotheses Testing Terminology 8.1.2 Testing Procedures 8.2 Tests Concerning Means and Variances 8.2.1 Tests About One Population Mean 8.2.2 Testing One Population Variance 8.2.3 Comparing Two Population Means 8.2.4 Comparing Two Population Variances 8.3 Duality Between Confidence Interval and Hypothesis Testing Exercises Chapter 9 Understanding Monte Carlo Method and Statistics Software 9.1 Monte Carlo Method 9.1.1 The Monte Carlo Method 9.1.2 Bootstrap Procedures 9.2 Introduction of Statistics Software Appendix A Tables A.1 Standard Normal Curve Areas A.2 Critical Values for Chi-squared Distributions A.3 Critical Values for t-Distributions A.4 Critical Values for F-Distributions Bibliography |
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