《工科機率統計（英文版）》是2018年9月清華大學出版社出版的圖書，作者是魏軍強。
基本介紹
- 中文名：工科機率統計（英文版）
- 作者：魏軍強
- 出版社：清華大學出版社
- 出版時間：2018年9月
- 定價：49 元
- ISBN：9787512137233
內容簡介,圖書目錄,
內容簡介
Probability and Statistics is a mathematical discipline which studies stochastic phenomena. Now it is widely used in industry, economics, science and technologies. This course is one of the important basic courses for engineering majors in comprehensive universities. The textbook will include the general conceptions and methods about probability and statistics. The main topics are as the following.
Basic probability concepts; Random experiment; Sample spaces; Rules of probability; Counting techniques; Conditional probability; Independence. Discrete and continuous random variables. Sampling methods, Descriptive Statistics, Sampling distributions, The Student-t distribution, F-distribution and Chi-Square distribution, Point estimation. Confidence intervals. Testing hypotheses. Statistical software like Excel and/or Matlab will be used.
圖書目錄
Chapter 1 Probability and Its Properties 1
1.1 Basic Probability Concepts 1
1.2 Axioms and Properties of Probability 4
1.2.1 Axioms Definition of Probability 5
1.2.2 Properties of Probability 5
1.3 Classical Probability and Counting Techniques 7
1.3.1 Counting Principles 7
1.3.2 Classical Probability 8
1.4 Conditional Probability, Independence of Two and Several Events 9
1.4.1 Conditional Probability 10
1.4.2 Independence 12
1.5 Law of Total Probability and Bayes’ Theorem 14
Exercises 17
Chapter 2 Random Variables and Their Distributions 20
2.1 Random Variables 20
2.2 Distribution of a Random Variable and Distribution Function 21
2.3 Classical Discrete Random Variables and Continuous Random Variables 27
2.3.1 Discrete Distribution 27
2.3.2 Continuous Distribution 31
2.4 Distribution of Functions of a Random Variable 36
Exercises 40
Chapter 3 Random Vectors and Their Distributions 44
3.1 Jointly Distributed Random Variables 44
3.2 Marginal Distribution and Conditional Distribution of Two Random Variables 49
3.3 Independent Random Variables 58
3.4 Distribution of Functions of Two Random Variables 63
Exercises 72
Chapter 4 Expectations and Moments 77
4.1 Mathematical Expectation and Its Properties 77
4.1.1 Mathematical Expectation 77
4.1.2 Properties of the Expectation 83
4.2 Variance and Its Properties 84
4.2.1 Definition of the Variance 84
4.2.2 Properties of the Variance 86
4.3 Expectations and Variances of Special Probability Distributions 87
4.3.1 Case for Common Discrete Random Variables 87
4.3.2 Case for Common Continuous Random Variables 89
4.4 Moments 91
4.4.1 Covariance and Correlation Coefficients 91
4.4.2 Moments 99
Exercises 101
Chapter 5 The Law of Large Numbers and the Central Limit Theorem 105
5.1 The Law of Large Numbers and Its Applications 105
5.1.1 Chebyshev’s Inequality 105
5.1.2 The Law of Large Numbers 107
5.2 The Central Limit Theorem and Its Applications 110
Exercises 112
Chapter 6 Basic Conceptions of Statistics 115
6.1 Basic Conceptions of Sampling 115
6.2 Descriptive Statistics 116
6.2.1 Summarizing Data—Numerical Methods 116
6.2.2 Summarizing Data—Graphical Methods 127
6.3 Fundamental Sampling Distributions 132
6.3.1 The Chi-squared Distribution 135
6.3.2 The t-Distribution 136
6.3.3 The F-Distribution 138
6.4 Sampling Distribution Theorems 140
Exercises 143
Chapter 7 Parameter Estimation 146
7.1 General Concepts of Point Estimation 146
7.2 Methods of Point Estimation 147
7.2.1 Method of Moments 147
7.2.2 Method of Maximum Likelihood Estimation 150
7.3 Criteria for Good Estimators 157
7.4 Interval Estimation 164
7.4.1 Confidence Intervals Based on a Single Sample 164
7.4.2 Confidence Intervals Based on Two Samples 169
7.5 One-sided Confidence Intervals (Confidence Bounds) 171
Exercises 172
Chapter 8 Hypothesis Testing 177
8.1 Hypotheses and Testing Procedures 177
8.1.1 Hypotheses Testing Terminology 178
8.1.2 Testing Procedures 182
8.2 Tests Concerning Means and Variances 183
8.2.1 Tests About One Population Mean 183
8.2.2 Testing One Population Variance 188
8.2.3 Comparing Two Population Means 189
8.2.4 Comparing Two Population Variances 190
8.3 Duality Between Confidence Interval and Hypothesis Testing 192
Exercises 194
Chapter 9 Understanding Monte Carlo Method and Statistics Software 199
9.1 Monte Carlo Method 199
9.1.1 The Monte Carlo Method 200
9.1.2 Bootstrap Procedures 201
9.2 Introduction of Statistics Software 202
Appendix A Tables 205
A.1 Standard Normal Curve Areas 205
A.2 Critical Values for Chi-squared Distributions 206
A.3 Critical Values for t-Distributions 207
A.4 Critical Values for F-Distributions 209
Bibliography 215
