1. Students are expected to learn about some important topics in inferential statistics such as the estimation, confidence interval, hypothesis testing, optimal tests and sufficient statistics.
2. Students should understand some basic definitions, terms and theorems in each topic including type I error, type II error, the power of a test, powerful tests, the central limit theorem, and the Neyman-Pearson theorem..
3. Students need to know how to apply their knowledge learned from each topic to solve relevant problems in their daily life.
4. In order to promote their understanding and efficiency, students are expected to use technology and software as tools to support their learning.
1. Teacher-centered: Explication of procedures, concepts and theory
2. Students-centered: Understanding, practice on skills and applications
1. Regular homework and quizzes (30%)
2. Midterm test (30%)
3. Final test (40%)
(1) Continuous random variables and their probability distribution including the normal distribution.(1 week).
(2) Multivariate probability distributions (1 week).
(3) Functions of random variables (1 week).
(4) Sampling distribution and the central limit theorem (2 weeks).
(5) Estimation (2 weeks).
(6) Properties of point estimators and methods of estimation (2 weeks).
(7) Hypothesis testing (3 weeks).
(8) Optimal tests (3 weeks).
(9) Sufficient statistics (3 weeks).
1. Robert Hogg; Allen Craig; Joseph McKean. (2004). Introduction to Mathematical Statistics, Sixth Edition. Prentice Hall, Englewood Cliffs, New Jersey, USA. (Textbook).
2. Steven F. Arnold, (1995). Mathematical Statistics. Prentice –Hall, Englewood Cliffs, New Jersey, USA.
3. William Mendenhall, Dennis Wackerly, Richard Scheaffer, (1990). Mathematical Statistics with Applications. PWS-KENT Publishing Company, Boston, Massachusetts, USA.
4. V.K. Rohatgi, An Introduction to Probability Theory and Mathematical Statistics. John Wiley & Sons, Inc., USA.