概率论与数理统计
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天津西青
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作者王彩凤 编
出版社冶金工业出版社
ISBN9787502484460
出版时间2020-04
装帧平装
开本32开
定价29元
货号1202078602
上书时间2024-10-18
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目录
Part A Probability and Random Variables
1 Axioms of Probability
1. i Introduction
1.2 Sample Space and Events
1.3 The Relative Frequency Definition of Probability
1.4 Axioms of Probability
1.5 Sample Spaces Having Equally Likely Outcomes
1.6 Conditional Probability
1.7 The Law of Total Probability (Partition Theorem)
1.8 Bayes Theorem
Exercises
2 Random Variables and Their Distributions
2. 1 Random Variables
2. 2 Discrete Random Variables
2.3 Some Important Discrete Probability Distributions
2. 3.1 Uniform Distribution (Discrete Case)
2.3.2 Bernoulli Trial
2. 3.3 Binomial Distribution
2.3.4 Poisson Distribution
2.3.5 Geometric Distribution
2. 4 Cumulative Distribution Functions
2.5 Continuous Random Variables
2.6 Some Important Continuous Probability Distributions
2. 6. 1 Uniform Distribution (Continuous Case)
2.6. 2 Normal Distribution
2.6. 3 Exponential Distribution
2. 7 Distributions of Functions of a Random Variable
Exercises
3 Multivariate Random Variables
3.1 Joint Distribution Function
3.1.1 Joint Distribution Function: Discrete Case
3.1.2 Joint Distribution Function: Continuous Case
3.2 Independent Random Variables
3.3 Conditional Distributions
3.3.1 Conditional Distributions: Discrete Case
3.3.2 Conditional Distributions: Continuous Case
3.4 Two Particular Multivariate Distribution
3.4. 1 Uniform Distribution
3.4.2 Bivariate Normal Distribution
3.5 Distributions of Spe Functions of Two Random Variables
3.5.1 Discrete Multivariate Random Variable
3.5.2 Continuous Multivariate Random Variable
Exercises
4 The Expectation and Variance
4. 1 Expectations of Random Variables
4. 2 The Variance of Random Variables
4. 3 Some Important Expectations and Variance
4. 3.1 Uniform Distribution (Discrete Case)
4.3.2 Binomial Distribution
4.3.3 Poisson Distribution
4. 3.4 Uniform Distribution (Continuous Case)
4.3.5 Exponential Distribution
4.3.6 Normal Distribution
4.4 Covariance and Correlation
4.4. 1 Covariance
4. 4. 2 Correlation Coefficient
Exercises
5 The Law of Large Numbers and the Central Limit Theorem
5. 1 Chebyshevs Inequality
5.2 Law of Large Numbers
5.3 The Central Limit Theorem
Exercises
Part B Statistical Inference
6 Sampling Distributions of Estimators
6. 1 Random Sampling
6. 2 Some Important Statistics
6.2. 1 Sample Mean
6.2.2 Sample Variance
6. 2. 3 Sample Standard Deviation
6. 3 Sampling Distributions
6. 3.1 Chi-squared Distribution
6. 3.2 t-Distribution
6.3.3 F-Distribution
Exercises
7 Parameter Estimation
7.1 Point Estimation
7.1.1 Method of Moments
7. 1.2 Method of Maximum Likelihood
7.2 The Particular Properties of Estimators
7.2. 1 Unbiasedness
7.2. 2 Efficiency
7.2.3 Consistency
7.3 Interval Estimation
7.3.1 Estimation of Means
7.3.2 Estimation of Variances
Exercises
8 Hypothesis Testing
8.1 Introduction
8.2 Tests Concerning Mean
8.3 Tests Concerning Variance
8.4 p-Values
Exercises
References
Appendix
Appendix A Tables
Appendix B Answers to Selected Exercises
Subject Index
内容摘要
本书采用学生易于接受的知识结构方式和英语表述方式，科学、系统地介绍了概率论与数理统计中随机事件、概率的三个定义、古典概率的计算、条件概率、全概率以及贝叶斯定理、一维随机变量及概率分布、二维随机变量及其分布、随机变量的数字特征、大数定律和中心极限定理、样本及抽样分布、参数估计、假设检验、线性回归、方差分析等知识。本书强调通用性和适用性，兼顾优选性，起点低，难度适中，语言简洁明了，不仅适用于课堂教学使用，同时也适用于自学自习。全书每章有习题配置，题量适中，题型全面，书后附有答案。本书读者对象为高等院校理工、财经、医药、农林等专业大学生和教师，特别适合作为中外合作办学的靠前教育班的学生以及准备出国留学深造学生的参考书。
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