大学理工
概率论与数理统计精品课（浙江大学）
课程目录
- 引言
- 1.1 General methodology of modern
- 1.2 Roles of Econometrics
- 1.3 Illustrative Examples
- 1.4 Roles of Probability and Statistics
- 2.0 Foundation of Probability Theory
- 2.1 Random Experiments
- 2.2 Basic Concepts of Probability
- 2.3 Review of Set Theory
- 2.4 Fundamental Probability Laws
- 2.5 Methods of Counting
- 2.6 Conditional Probability
- 2.7 Bayes_ Theorem
- 2.8 Independence
- 2.9 Conclusion
- 3.0 Random Variables and Univariate Probability
- 3.1 Random Variables
- 3.2 Cumulative Distribution Function
- 3.3 Discrete Random Variables(DRV)
- 3.4 Continuous Random Variables
- 3.5 Functions of a Random Variable
- 3.6 Mathematical Expectations
- 3.7 Moments
- 3.8 Quantiles
- 3.9 Moment Generating Function (MGF)
- 3.10 Characteristic
- 3.11 Conclusion
- 4.1 Important Probability Distributions
- 4.2 Discrete Probability Distributions
- 4.3 Continuous Probability Distributions
- 4.4 Conclusion
- 5.0 Multivariate Probability Distributions
- 5.1 Random Vectors and Joint Probability Distributions
- 5.2 Marginal Distributions
- 5.3 Conditional Distributions
- 5.4 Independence
- 5.5 Bivariate Transformation
- 5.6 Bivariate Normal Distribution
- 5.7 Expectations and Covariance
- 5.8 Joint Moment Generating Function
- 5.9 Implications of Independence on Expectations
- 5.10 Conditional Expectations
- 5.11 Conclusion
- 概率论与统计学 上期复习与本期导学
- 6.0 Introduction to Statistic
- 6.1 Population and Random Sample
- 6.2 Sampling Distribution of Sample Mean
- 6.3 Sampling Distribution of Sample Variance
- 6.4 Student’s t-Distribution
- 6.5 Snedecor_s F Distribution
- 6.6 Sufficient Statistics
- 6.7 Conclusion
- 7.0 Convergences and Limit Theorems
- 7.1 Limits and Orders of Magnitude-A Review
- 7.2 Motivation for Convergence Concepts
- 7.3 Convergence in Quadratic Mean and Lp-Convergence
- 7.4 Convergence in Probability
- 7.5 Almost Sure Convergence
- 7.6 Convergence in Distribution
- 7.7 Central Limit Theorems_batch
- 8.1 Population and Distribution Model
- 8.2 Maximum Likelihood Estimation
- 8.3 Asymptotic Properties of MLE
- 8.4 Method of Moments and Generalized Method of moments
- 8.5 Asymptotic Properties of GMM
- 8.6 Mean Squared Error Criterion
- 8.7 Best Unbiased Estimators
- 8.8 Cramer-Rao Lower Bound
- 9.1 Introduction to Hypothesis Testing
- 9.2 Neyman-Pearson Lemma
- 9.3 Wald Test
- 9.4 Lagrangian Multiplier (LM) Test
- 9.5 Likelihood Ratio Test
- 9.6 Illustrative Examples
- 10.1 Big Data Machine Learning and Statistics
- 10.2 Empirical Studies and Statistical Inference
- 10.3 Important Features of Big Data
- 10.4 Big Data Analysis and Statistics
- 讲座：概率论与统计学在经济学中的应用
课程介绍
《概率论与数理统计》是食品、工科、农科、经管类等专业开设的专业必修课程中重要的内容，学时数48学时，3学分.是基础课，是主干课之一.该课程的任务是要使学生正确理解和掌握概率论与数理统计的基本概念，基本理论，基本掌握概率论与数理统计中的论证方法，较熟练地获得本课程所要求的基本计算方法和能力，增强运用数学手段解决实际问题的能力，为进一步学习计算机应用技术专业的后继课程打下必要的基础.
概率论与数理统计的教学内容主要涉及随机事件与概率、一元与多元随机变量及其分布、随机变量的数字特征、数理统计的基本概念、参数估计与假设检验 、方差分析与回归分析六大知识体系。在教学内容的组织上以近代概率论的内容为基础,侧重于讲解概率论与数理统计的基本理论与方法，同时在教学中注注重理论联系实际，结合各专业的特点介绍性地给出在各领域中的具体应用案例，帮手学生正确理解和使用这些方法。别的在教学中适当增加了数学实验的内容，介绍统计软件包SAS或Excel在数理统计中的应用，使用现代化的先进的计算机软件的模拟和计算速度的功能，形象、生动的去验证和表示相关理论。使课程内容的设计更具有科学性、先进性，符合教育教学的规律。
