The objective of this course is intended to introduce theoretical statistics for undergraduate students majoring in statistics. The emphases will be on




НазваниеThe objective of this course is intended to introduce theoretical statistics for undergraduate students majoring in statistics. The emphases will be on
Дата08.10.2012
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科 目:1389數理統計 (96學年上學期之授課大綱)   

教 師:王榮琮




科目名稱: 數理統計 1389

1. Course Description:
The objective of this course is intended to introduce theoretical statistics for undergraduate students majoring in statistics. The emphases will be on understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations. Topics include probability theory, common families of distributions, properties of a random sample (especially on convergence concepts), principles of data reduction (sufficiency, likelihood), point estimation (finding and evaluating estimators), hypothesis testing (finding and evaluating tests), interval estimation, and Bayesian statistics.


2. Course Outline:
Chapter 1: Probability and Distributions
1.1 Introduction
1.2 Set Theory
1.3 The probability Set Function
1.4 Conditional Probability and Independence
1.5 Random Variables
1.6 Discrete Random Variables (Transformations)
1.7 Continuous Random Variables (Transformations)
1.8 Expectation of a Random Variable
1.9 Some Special Expectations
1.10 Important Inequalities
Chapter 2: Multivariate Distributions
2.1 Distributions of Two Random Variables
2.2 Transformations of Bivariate Random Variables
2.3 Conditional Distributions and Expectations
2.4 The Correlaion Coefficient
2.5 Independent Random Variables
2.6 Extension to Several Random Variables
2.7 Transformations of Random Vectors
Chapter 3: Some Special Distributions
3.1 The Binomial and Related Distributions
3.2 The Poisson Distribution
3.3 The gamma, chi-square, and beta Distributions
3.4 Te Normal Distribution
3.5 The Multivariate Normal Distribution
3.6 t and F-Distributions
3.7 Mixture Distributions
Chapter 4: Unbiasedness, Consistency, and Limiting Distributions
4.1 Expectations of Functions
4.2 Convergence in Probbaility
4.3 Convergence in Distribution
4.4 Central Limit Theorem
4.5 Asymptotics for Multivariate Distributions
Chapter 5: Some Elementary Statistical Inferences
5.1 Sampling and Statistics
5.2 Order Statistics
5.3 Tolerance Limits for Distributions
5.4 More on Confidence Intervals
5.5 Introduction to Hypthesis Testing
5.6 Additional Comments About Statistical Tests
5.7 Chi-Square Tests
5.8 The Method of Monte Carlo
5.9 Bootstrap Procedures


3.1 Textbook:
1. Robert V. Hogg, Joseph W. McKean, Allen T. Craig (2005) Introduction to Mathematical Statistics (6/E), Pearson Prentice Hall.


3.2 Reference Books:
1. Lee J. Bain, Max Engelhardt (1992) Introduction to Probability and
Mathematical Statistics (2/E), Duxbury Press.
2. George G. Roussas (1997) A Course in Mathematical Statistics (2/E),
Addison-Wesley
3. R.V. Hogg, E.A. Tanis (2005) Probability and Statistical Inference
(7/E), Prentice Hall.
4. R.J. Laesen, M.L. Marx (2006) An Introduction to Mathematical
Statistics and Its Applications (4/E), Pearson Education International.


4. Assessment: Mid-term exam (35%), Final exam (40%), Quiz (25%)




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