- 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
- 概率論與統(tǒng)計(jì)學(xué) 上期復(fù)習(xí)與本期導(dǎo)學(xué)
- 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
- 講座:概率論與統(tǒng)計(jì)學(xué)在經(jīng)濟(jì)學(xué)中的應(yīng)用
《概率論與數(shù)理統(tǒng)計(jì)》是食品、工科、農(nóng)科、經(jīng)管類等專業(yè)開(kāi)設(shè)的專業(yè)必修課程中重要的內(nèi)容,學(xué)時(shí)數(shù)48學(xué)時(shí),3學(xué)分.是基礎(chǔ)課,是主干課之一.該課程的任務(wù)是要使學(xué)生正確理解和掌握概率論與數(shù)理統(tǒng)計(jì)的基本概念,基本理論,基本掌握概率論與數(shù)理統(tǒng)計(jì)中的論證方法,較熟練地獲得本課程所要求的基本計(jì)算方法和能力,增強(qiáng)運(yùn)用數(shù)學(xué)手段解決實(shí)際問(wèn)題的能力,為進(jìn)一步學(xué)習(xí)計(jì)算機(jī)應(yīng)用技術(shù)專業(yè)的后繼課程打下必要的基礎(chǔ).
概率論與數(shù)理統(tǒng)計(jì)的教學(xué)內(nèi)容主要涉及隨機(jī)事件與概率、一元與多元隨機(jī)變量及其分布、隨機(jī)變量的數(shù)字特征、數(shù)理統(tǒng)計(jì)的基本概念、參數(shù)估計(jì)與假設(shè)檢驗(yàn) 、方差分析與回歸分析六大知識(shí)體系。在教學(xué)內(nèi)容的組織上以近代概率論的內(nèi)容為基礎(chǔ),側(cè)重于講解概率論與數(shù)理統(tǒng)計(jì)的基本理論與方法,同時(shí)在教學(xué)中注注重理論聯(lián)系實(shí)際,結(jié)合各專業(yè)的特點(diǎn)介紹性地給出在各領(lǐng)域中的具體應(yīng)用案例,幫助學(xué)生正確理解和使用這些方法。另外在教學(xué)中適當(dāng)增加了數(shù)學(xué)實(shí)驗(yàn)的內(nèi)容,介紹統(tǒng)計(jì)軟件包SAS或Excel在數(shù)理統(tǒng)計(jì)中的應(yīng)用,使用現(xiàn)代化的先進(jìn)的計(jì)算機(jī)軟件的模擬和計(jì)算速度的功能,形象、生動(dòng)的去驗(yàn)證和表現(xiàn)相關(guān)理論。使課程內(nèi)容的設(shè)計(jì)更具有科學(xué)性、先進(jìn)性,符合教育教學(xué)的規(guī)律。
