Course Title | Statistics | ||
Course Code | MH3500 | ||
Offered | Study Year 2, Semester 2 | ||
Course Coordinator | Yeo Kwee Poo (Asst Prof) | kweepoo@ntu.edu.sg | 6513-7456 |
Pre-requisites | MH2500 | ||
AU | 4 | ||
Contact hours | Lectures: 39, Tutorials: 12 | ||
Approved for delivery from | AY 2022/23 semester 2 | ||
Last revised | 28 Nov 2022, 22:30 |
This course aims to develop your understanding of the statistical concepts of parameter estimation and hypothesis testing that are fundamental for real life applications of statistics as well as for numerous further courses in the curriculum of the statistics track.
Upon successfully completing this course, you should be able to:
Review of probability
Random samples, sample mean and sample variance, distributions derived from the normal distribution, Central Limit Theorem and its significance for statistics
Introduction to parameter estimation, quality criteria for parameter estimators
Constructing good estimators: method of moments and maximum likelihood method
Asymptotic properties of estimators, Cramer-Rao bound and efficient estimators
Confidence intervals for estimators
Introduction to hypothesis testing and Fisher-type tests
Neyman-Pearson tests and Neyman-Pearson Lemma
Component | Course ILOs tested | SPMS-MAS Graduate Attributes tested | Weighting | Team / Individual | Assessment Rubrics |
---|---|---|---|---|---|
Continuous Assessment | |||||
Tutorials | |||||
Assignment | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 | 1. a, b, c 2. c 3. a | 20 | individual | See Appendix for rubric |
Mid-semester Quiz | |||||
Short Answer Questions | 1, 2, 3, 4, 5 | 1. a, b, c 2. c 3. a | 20 | individual | See Appendix for rubric |
Examination (2 hours) | |||||
Short Answer Questions | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 | 1. a, b, c 2. c 3. a | 60 | individual | See Appendix for rubric |
Total | 100% |
These are the relevant SPMS-MAS Graduate Attributes.
1. Competence
a. Independently process and interpret mathematical theories and methodologies, and apply them to solve problems
b. Formulate mathematical statements precisely using rigorous mathematical language
c. Discover patterns by abstraction from examples
2. Creativity
c. Develop new applications of existing techniques
3. Communication
a. Present mathematics ideas logically and coherently at the appropriate level for the intended audience
Midterm exam: Feedback on common mistakes and the level of difficulty of the problems is given.
Assignment: Students will receive individual feedback on their performance in the assignments during the tutorial sessions.
Lectures (39 hours) | The lectures cover the basic theory of parametric statistics using the following approach: - Illustration of concepts and theorems by numerous examples |
Tutorials (12 hours) | Two types of tutorial problems will be given: 1) Problems that test comprehension of basic definitions and theorems. 2) More advanced problems that either require quite strong computational and reasoning skills or creativity in coming up with mathematical proofs. |
John A. Rice: Mathematical Statistics and Data Analysis, Third Edition,
ISBN-13: 978-8131519547
ISBN-10: 8131519546
Absence Due to Medical or Other Reasons
If you are sick and not able to attend a quiz or midterm, you have to submit the original Medical Certificate (or another relevant document) to the administration to obtain official leave. In this case, the missed assessment component will not be counted towards the final grade. There are no make-up quizzes or make-up midterm.
Good academic work depends on honesty and ethical behaviour. The quality of your work as a student relies on adhering to the principles of academic integrity and to the NTU Honour Code, a set of values shared by the whole university community. Truth, Trust and Justice are at the core of NTU’s shared values.
As a student, it is important that you recognize your responsibilities in understanding and applying the principles of academic integrity in all the work you do at NTU. Not knowing what is involved in maintaining academic integrity does not excuse academic dishonesty. You need to actively equip yourself with strategies to avoid all forms of academic dishonesty, including plagiarism, academic fraud, collusion and cheating. If you are uncertain of the definitions of any of these terms, you should go to the Academic Integrity website for more information. Consult your instructor(s) if you need any clarification about the requirements of academic integrity in the course.
Instructor | Office Location | Phone | |
---|---|---|---|
Yeo Kwee Poo (Asst Prof) | SPMS-MAS-04-16 | 6513-7456 | kweepoo@ntu.edu.sg |
Week | Topic | Course ILO | Readings/ Activities |
---|---|---|---|
1 | Review of probability | 1 | Study lecture notes |
2 | Review of probability | 1 | Study lecture notes |
3 | Random samples, sample mean and sample variance, distributions derived from the normal distribution, Central Limit Theorem and its significance for statistics | 2, 3 | Study lecture notes |
4 | Introduction to parameter estimation, quality criteria for parameter estimators | 5 | Study lecture notes |
5 | Constructing good estimators: method of moments and maximum likelihood method | 4 | Study lecture notes |
6 | Constructing good estimators: method of moments and maximum likelihood method | 4 | Study lecture notes |
7 | Constructing good estimators: method of moments and maximum likelihood method | 4 | Study lecture notes |
8 | Asymptotic properties of estimators, Cramer-Rao bound and efficient estimators | 6 | Study lecture notes |
9 | Asymptotic properties of estimators, Cramer-Rao bound and efficient estimators | 6 | Study lecture notes |
10 | Confidence intervals for estimators | 7 | Study lecture notes |
11 | Introduction to hypothesis testing and Fisher-type tests | 8 | Study lecture notes |
12 | Neyman-Pearson tests and Neyman-Pearson Lemma | 9, 10, 11 | Study lecture notes |
13 | Neyman-Pearson tests and Neyman-Pearson Lemma | 9, 10, 11 | Study lecture notes |