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Introduction to the Probability and Statistics
Course No： 02834720 Program：Undergraduate
Credit：4 Instructor：Zhang Junni & Song Xiaojun Prerequisite： Calculus, Linear Algebra Semester：2016 Spring
Instructor’s resume/brief introduction(Within 500 words) Zhang junni is now associate Professor, Department of Business Statistics and Econometrics, Guanghua School of Management, Peking University. She graduated from University of Science and Technology of China and received bachelor degree in Computer Software. In 2002, she achieved her Ph.D in statistics from Harvard University. Now her research interest focuses on areas like Causal Inference in Social Sciences, Monte Carlo Methods, Data Mining and Applied Statistics. Her papers have been adopted by many international top journals, such as Journal of the American Statistical Association, Journal of Educational and Behavioral Statistics, Statistica Sinica, Computational Statistics and Data Analysis, Journal of Chemical Physics. Now she is member of American Statistical Association and International Chinese Statistics Association. She is teaching courses like Probability , Mathematical Statistics, Quantitative Methods in Management, Data Mining and Applications, Hierarchical Linear Models and Statistical Analysis for Business. 宋晓军，北京大学光华管理学院商务统计与经济计量系助理教授。毕业于马德里卡洛斯三世大学经济系，获经济学博士学位。研究方向是理论计量经济学和应用计量
经济学。 Instructor’s contact information Zhang Junni:Office: Room 473 in Guanghua Building #2. Tel: 62757922. E-mail: [email protected]. Song Xiaojun: 办公电话：86-10-62754839 Email：[email protected] TA’s contact information Office hour
Program Learning Goals and Objectives
Learning Goal 1: Graduates will possess a solid understanding of business and management and will be able to translate this knowledge into practice.
1.1 Objective 1 Our students will have a good command of fundamental theories and
knowledge. 1.2 Objective 2 Our students will have a good command of analytical methods and
decision-making tools. 1.3 Objective 3 Our students will be able to apply theories and methodologies in key
business functions. Learning Goal 2: Our students will be able to think critically.
2.1 Objective 1 Our students will be able to identify and summarize problems 2.2 Objective 2 Our students will be able to collect data and analyze problems in a
critical manner 2.3 Objective 3 Our students will be able to put forward effective solutions to business
problems Learning Goal 3: Our students will have a sense of social responsibility.
3.1 Objective 1 Our students will be aware of the importance of ethics. 3.2 Objective 2 Our students will be able to provide solutions that take account of
contrasting ethical standpoints. Learning Goal 4: Our students will be effective communicators.
4.1 Objective 1 Our students will be proficient in oral and written communication. 4.2 Objective 2 Our students will possess good interpersonal skills. 4.3 Objective 3 Our students will be able to adapt to diverse learning environments.
Learning Goal 5: Our students will have global perspectives. 5.1 Objective 1 Our students will be aware of social and cultural differences. 5.2 Objective 2 Our students will be aware of the impact of globalization on business
operations, opportunities, and challenges. 5.3 Objective 3 Our students will be proficient in English.
This course will introduce basics of probability theory and mathematical statistics, including probability, conditional probability, random variable, expectation and variance, special probability distributions, sampling distribution, point estimation, confidence interval, hypothesis testing, linear regression, analysis of variance, etc.
Course Overview
Students should understand basic concepts in probability theory and mathematical statistics, learn commonly used probability distributions, and be able to conduct basic statistical inferences.
Coure Objectives
Lecture No.
Detailed Course Plan
Topics
Assignments 1 Experiments and Events. Set Theory. The Definition of
Probability.
2 Finite Sample Space. The Probability of a Union of Events.
Homework 1
3 The Definition of Conditional Probability. Independent Events.
4 Conditionally Independent Events. Bayes’ Theorem. Homework 2 5 Random Variables. Discrete Distributions. Continuous
Distributions.
6 Bivariate Distributions. Marginal Distributions. Independence of two random variables.
Homework 3
7 Conditional Distributions. Multivariate Distributions. 8 Functions of a Random Variable. Functions of Two or
More Random Variables. Homework 4
9 Expectation. Properties of expectation. Bernoulli, Binomial and Poisson Distributions, and their Expectations.
10 Variance. Properties of Variance. The variances of Bernoulli, Binomial and Poisson Distributions. The Exponential Distribution.
Homework 5
11 Covariance and Correlation. The Sample Mean. 12 The Normal Distribution. The Central Limit Theorem. Homework 6 13 Conditional Expectation and Variance. Bivariate
Normal Distribution.
14 Descriptive Statistics. Homework 7 15 Statistical Inference. The Likelihood Function and
Maximum Likelihood Estimators.
16 Unbiased Estimators. Precision of Point Estimators. The Sampling Distribution of a Statistic.
Midterm Exam (Covering Material in Lectures 1-13)
17 The Chi-Square Distribution. Joint Distribution of the Sample Mean and Sample Variance. The t Distribution.
Homework 8
18 Confidence Intervals. 19 Basics of Hypothesis Testing. Homework 9 20 Testing for Mean When Variance is Known and Testing
for Probability. p value. Equivalence of Tests and Confidence Intervals.
21 The t Test. Paired t test. Homework 10 Team Project
22 Comparing the Means of Two Normal Distributions. The F Distribution. Comparing the Variances of Two Normal Distributions.
23 Test of Goodness of Fit. Contingency Tables Homework 11 24 Method of Least Squares. Simple Linear Regression. 25 Statistical Inference in Simple Linear Regression.
Prediction in Simple Linear Regression. Homework 12
26 Multiple Linear Regression.
27 Prediction in Multiple Linear Regression. Qualitative Independent Variables in Linear Regression. Analysis of Residuals. The Multicollinearity Issue.
Homework 13
Final Exam：2016.6.15
Lectures, Q&A and team project. Teaching Methods
Powerpoint presentations will be used in the classroom. Excel will be used for demonstration at times.
IT tools to be used in the classroom
R will be taught at the exercise sessions.
Morris H. DeGroot and Mark Schervish (2001), Probability and Statistics, Addison Wesley, 3rd edition.
Textbooks
Probability and Statistics, Revised Edition by Xiangzhong Fang, Ligang Lu, Dongfeng Li, Higher Education Press, 2005.
1. Lecture notes. References & Readings
2. Reference books: (a) John A. Rice (1994), Mathematical Statistics and Data Analysis, 2nd edition, Duxbury Press. (b) 陈家鼎等 (1993)，《数理统计学讲义》，高等教育出版社。 (c) 戴维 R. 安德森，丹尼斯 J. 斯维尼，托马斯 A. 威廉斯 著，张建华等译，《商务
与经济统计》，机械工业出版社。
Videos, CD-ROMs and other adjunct learning resources used
Rules students must follow
Your final grade will be based on four components: Course Assessment
1. Individual weekly homework account for 30%. You may discuss homework problems with other students, but you must write them up
independently. Homework is due at the beginning of class on the due date. Note that homework that is turned in later than the end of class on the due date will not be graded. It is understood that sometimes your schedule may not allow you to turn in your homework on time, so your lowest homework score will be dropped when computing your final homework grade.
2. Team project will account for 10%. 3. Individual midterm exam will account for 33%. 4. Individual final exam will account for 33%. Note that cheating is strictly not allowed and will result in zero score on the respective part.
How does this course serve the Assurance of Learning Assessment? （Macro-Economics; Corporate Finance; International Finance and International Trade）
