Download HE1005 Introduction to Probability and Statistical Inference

HE1005 Introduction to Probability and Statistical Inference
Nanyang Technological University
Division of Economics
Spring 2015
Prof. Leong Kaiwen Leong Office
Email: [email protected]
Phone: (+65)67906735
Office: HSS-04-52
Office Hours: Friday 1130 to 1230 and by appointment
Lecture: Friday 0930 to 1130
Course Objectives
This course is an intermediate level probability and statistics course with a
focus on the theoretical foundations of statistical inference. The primary
objective is to provide an introduction to mathematical statistics necessary for
the subsequent study of econometrics and economic theory. Univariate and
multivariate models are covered, and matrix algebra is used extensively. A
brief review of the most important results in matrix algebra is provided at the
beginning of the course. The course does not cover measure theoretic
probability but some terminology from measure theory is introduced.
Prerequisites
No prior preparation in probability and statistics is required, but familiarity with
algebra and calculus is assumed. There are no formal prerequisites.
Required Text
Hogg, McKean and Craig (2013), Introduction to Mathematical Statistics,
Pearson, Seventh Edition (IMS). The book is available at the NTU bookstore.
Additional References
Casella, G., and R. Berger (2002), Statistical Inference, Duxbury Press,
Second Edition. This book contains a lot more theoretical examples as
compared to the Introduction to Mathematical Statistics.
Requirements and Grading
There will be weekly homework assignments, one midterm and one final. The
course grade will be determined by the midterm (40%) and the final (60%). The
weekly problem sets will be posted on blackboard. While the problems sets will
not be graded or collected. Their solutions will be discussed in tutorials and
they are part of the material that you will be tested on for both examinations.
You are encouraged to work in groups for the homework.
If you miss the midterm examination, please produce a medical certificate and
submit it to the division of economics. Also notify me via email. In this instance,
your final grade will be solely determined by your performance on the final
exam. If you miss an exam without a medical certificate that is acceptable to
the division of economics, you will score zero points for the exam. There are
no exceptions to this rule.
Lectures
It is expected that all students attend all lectures and the weekly discussion
sessions. If you miss any classes for any reasons, it is your duty to get the
required notes from your classmates. Please check the course blackboard
website everyday for any class announcements.
Office Hours
Students are encouraged to take advantage of the instructor’s office hours to
clarify material covered in class and other matters related to the course. If you
are unable to meet during regular office hours you should setup an
appointment with me via email.
The best way to contact me outside of office hours is via email. However,
please be aware that I cannot reply to questions that require lengthy answers
about material covered in the course. If you have such questions, please come
to my office and I will be happy to help you. I will try to respond to your short
questions within 48 hours. Please be aware that I do not respond to emails
over the weekends.
Exam Schedule
The final exam date is completely determined by the registrar’s office. I have
no control over this. The midterm exam will be held on the 7th lecture in class.
Academic Dishonestly/Misconduct
All cases of academic misconduct and dishonestly will not be tolerated. They
will be reported to the relevant authorities immediately. Please consult the
economics division or your student handbook to find out more about what
constitutes academic misconduct/dishonestly.
Course Outline
Please note that this is a preliminary outline. It is subject to changes.
The course covers the following topics. Required reading in the book (IMS) is
listed below for each topic. In addition to reading of the textbook, attendance of
lectures is essential.
Part I – Elements of Probability
1. Set Theory (IMS Chapter 1.1 and 1.2)
2. Definition of Probability (IMS Chapter 1.3)
3. Conditional Probability and Independence (IMS Chapter 1.4)
4. Random Variables, Distribution Functions, and Density and Mass Functions
(IMS Chapter 1.5 an 1.6)
5. Expectations and Moment Generating Functions (IMS Chapter 1.8)
6. Special Distributions (IMS Chapter 3.1 to 3.7)
7. Multivariate Distributions (IMS Chapter 2.1 and 2.6)
8. Transformations and Mixtures (IMS Chapter 2.2)
9. Multivariate Normal and Transformations (IMS Chapter 3.5)
10. Inequalities (IMS Chapter 1.10)
Part II – Elements of Statistical Inference
1. Random Samples and Statistics (IMS Chapter 4.1)
2. Sample Mean and Sample Variance (IMS Chapter 5.1)
3. Other sampling Schemes (IMS Chapter 5.2)
Part III –Statistical Inference
1. Point Estimation (IMS Chapter 4.2)
2. Hypothesis testing and Interval Estimation (IMS Chapter 4.5)