課程資訊

99-1

MATH7603

221 U1570

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/991statinference

Contents:
1.Probabilities, random variables, and distributions.
2.Transformations and expectations.
3.Common families of distributions.
4.Multivariate probability distributions and related properties.
5.Random samples, sampling distributions, and convergence concepts.
6.Sufficiency, likelihood, and equivalence principals.

The objective of this course is to introduce to the students some basic theory of probability. It is fundamentally important for understanding the commonly used statistical concepts and methods. It also provides a necessary basis for students for a further study of other advanced statistical courses.

Introduction to Probability and Statistics Theory or equivalent

Office Hours

Textbook and References:
1. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Press.
2. Bickel, P. S. and Doksum, K. A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I, 2nd ed. Prentice Hall.
3. Karr, A. F. (1993). Probability. Springer-Verlag.

(僅供參考)

 No. 項目 百分比 說明 1. Homeworks 20% 2. Midterm 30% 3. Final 30% 4. Quizzes 20%

 課程進度
 週次 日期 單元主題 第1週 9/16 Overview; Set Theory, Basics of Probability Theory 第2週 9/23 Conditional Probability and Independence, Random Variable, Density and Mass Functions 第3週 9/30 26日網路退選課程截止（系統開放至27日上午8時）; Distributions of Functions of a Random Variable, Expected values 第4週 10/07 Moments and moment generating functions, Differentiating under an integral sign 第5週 10/14 Discrete Distribution, 第6週 10/21 Continuous Distribution 第7週 10/28 Exponential Families, Location and Scale Families, Inequalities and Identities 第8週 11/04 Multiple Random Variables, Quiz 1 第9週 11/11 期中考週。Multiple Random Variables, Transformations, Hierarchical Models and Mixture Distributions, Covariance and Correlation 第10週 11/18 15日本校校慶(停課一天)。 Midterm, Multivariate Distribution, Inequlaity 第11週 11/25 Convergence Concepts 第12週 12/02 Sums of Random Variables from a Random Sample, Properties of the sample mean and variance 第13週 12/09 停修申請開始至12月10止。Order Statistics and Convergence Concepts, Generating a random sample 第14週 12/16 Sufficient Principle, Likelihood Principle, Quiz 2 (3:30-4:30; Chapter 4.4 to 4.6 and Chapter 5.1, 5.2, and 5.5) 第15週 12/23 Order Statistics and Convergence Concepts, 第16週 12/30 Sufficient Principle, Likelihood Principle, 第17週 01/06 Sufficient Principle, Likelihood Principle, 第18週 01/13 期末考試。