Download Introduction to Probability and Statistics Course No.: 02834720

Introduction to Probability and Statistics
Course No.: 02834720
Credit: 4
Prerequisite: Calculus, Linear Algebra
Program: Undergraduate
Instructor: Junni Zhang
Semester: 2014 Fall
Contact Information: Office: Room 473 in Guanghua Building #2. Tel: 62757922.
E-mail: [email protected].
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.
Brief Course Description
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.
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Course Objectives
Students should understand basic concepts in probability theory and mathematical
statistics, learn commonly used probability distributions, and be able to conduct basic
statistical inferences.
Detailed course plan (Outline of Units)
Lecture
No.
Topics
Assignments
1
Experiments and Events. Set Theory. The Definition of
Probability.
2
Finite Sample Space. The Probability of a Union of Homework 1
Events.
3
The Definition of Conditional Probability. Independent
Events.
4
Conditionally Independent Events. Bayes’ Theorem.
5
Random Variables. Discrete Distributions. Continuous
Distributions.
6
Bivariate Distributions. Marginal
Independence of two random variables.
7
Conditional Distributions. Multivariate Distributions.
8
Functions of a Random Variable. Functions of Two or
More Random Variables.
9
Expectation. Properties of expectation. Bernoulli,
Binomial and Poisson Distributions, and their
Expectations.
10
Variance. Properties of Variance. The variances of Homework 5
Bernoulli, Binomial and Poisson Distributions. The
Exponential Distribution.
11
Covariance and Correlation. The Sample Mean.
12
The Normal Distribution. The Central Limit Theorem.
13
Conditional Expectation and Variance. Bivariate
Normal Distribution.
14
Descriptive Statistics.
15
Statistical Inference. The Likelihood Function and
Maximum Likelihood Estimators.
16
Unbiased Estimators. Precision of Point Estimators.
The Sampling Distribution of a Statistic.
Distributions.
Homework 2
Homework 3
Homework 4
Homework 6
Homework 7
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.
2
Homework 8
18
Confidence Intervals.
19
Basics of Hypothesis Testing.
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.
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
24
Method of Least Squares. Simple Linear Regression.
25
Statistical Inference in Simple Linear Regression.
Prediction in Simple Linear Regression.
26
Multiple Linear Regression.
27
Prediction in Multiple Linear Regression. Qualitative
Independent Variables in Linear Regression. Analysis
of Residuals. The Multicollinearity Issue.
Homework 9
Homework 10
Team Project
Homework 11
Homework 12
Homework 13
Teaching Methods
Lectures, Q&A and team project.
IT tools to be used in the classroom (if any)
Powerpoint presentations will be used in the classroom. Excel will be used for
demonstration at times.
R will be taught at the exercise sessions.
Textbooks
Morris H. DeGroot and Mark Schervish (2001), Probability and Statistics,
Addison Wesley, 3rd edition.
Probability and Statistics, Revised Edition by Xiangzhong Fang, Ligang Lu,
Dongfeng Li, Higher Education Press, 2005.
References and readings
1. Lecture notes.
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。
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Course Assessment
Your final grade will be based on four components:
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.
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