課程資訊

106-1

MATH7603

221 U1570

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH7603_

Contents:
1. Probabilities, random variables, and distributions.
2. Transformations and expectations.
3. Common families of distributions.
4. Multivariate probability distributions and related concepts such as conditional distributions,
independence, and conditional expectation.
5. Random samples, sampling distributions, convergence concepts, and generating random samples.
6. Sufficiency, likelihood, and equivalence principals.
7. Best unbiased estimators

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
Students taking this course should be grounded in probability and mathematical
statistics at the upper division undergraduate level.

Office Hours

Textbook and References:
1. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Press.
2. Efron, B. and Hastie, Trevor (2016). Computer Age Statistical Inference: Algorithms, Evidence, and Data Science
3. Bickel, P. S. and Doksum, K. A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics,
Vol. I, 2nd ed. Prentice Hall.
4. 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 9/11, 14 Review of Basic Probability Theory: A1-A7 (Bickel and Doksum Vol 1 (2nd Edition) Probability on Euclidean Space (Talk about math tools associated with discrete RV and continuous RV. They are summation and integration (if its DF is absolutely continuous). 第2週 9/18, 21 24日網路加選課程截止（中午12時截止）Describing Data with the language of probability, often used probability distribution, moment and probability inequality, limit theorem, and type of convergence 第3週 9/25, 28, 30 停修申請開始(至12月9日止); 9/30 調整(10/09放假) Condition Probability and Simpson Paradox 第4週 10/2, 5 Moments and moment generating functions, Discrete Distribution (Binomial, Poisson) Continuous Distribution (Uniform, exponential) 第5週 10/12 10日 國慶紀念日(放假日); Differentiating under an integral sign. Finish up Chapter 3 and start on Chapter 4 on multiple random variables. 第6週 10/16, 19 週一: Differentiating under an integral sign, Exponential Families, Location and Scale Families. 週四: Inequalities and Identities, Start on Multiple random variables 第7週 10/23, 26 週一: 週四: Multiple random variables (joint and marginal distribution, conditional distribution and independence), Hierarchical models and mixture distributions, Bivariate transformations. 第8週 10/30, 11/02 Multiple Random Variables: Multiple Random Variables, Bivariate transformations, Hierarchical Models and Mixture Distributions, Covariance and Correlation; 第9週 11/6, 9 11/10 期中考 第10週 11/13 自主學習周, 本週停課 15日本校校慶(停課一天) 第11週 11/20, 23 On Monday, go over Definition 5.1.1. and Section 5.5 on Convergence Concepts. On Thursday, teach on generating a random sample (Chapter 5.6). 第12週 11/27, 30 Continue on Convergence Concepts and order statistics 第13週 12/4, 7 停修申請開始至12月7日止。Finish Ch5.5.1-5.5.3 and start on Delta method and concept on showing that MLE is a good estimation method. 第14週 12/11, 14 Start on Method of Moments (Chapter 7.2.1) and Maximum Likelihood Estimators (Chapter 6.3.1 and Chapter 7.2.2). 第15週 12/18, 21 Order Statistics, Method of Moments and Maximum Likelihood Estimate 第16週 12/25, 28 Estimation 第17週 1/04 No class on 1/01 第18週 1/11 週四: 期末考試。範圍為Chapters 4.4-5, 5, 6.3.1, and 7.2.1-7.2.2, 不含Metropolis Algorithm.