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課程名稱 |
統計學
Statistics |
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開課學期 |
103-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳 宏 |
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課號 |
MATH3601 |
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課程識別碼 |
201 38100 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一7,8(14:20~16:20)星期三2(9:10~10:00) |
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上課地點 |
天數304天數304 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1032MATH3601_stat |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
Contents:
1. Modern applications of statistics; Data exploration; Least squares estimation;
Use of R. (Chapters 7, 10 and 14)
2. Model formulation; Parametric models; Parameter estimation; Method of moments and
maximum likelihood; Assessment of fit. (Chapters 2, 3, 4, 5, 6, and 8)
3. Motivation by example and simulation (Chapters 2, 3, 4, 5, and 6)
4. Probability language: Description of random phenomenon, sampling variation,
assessment by simulation, sample mean and variance etc. (Chapters 1, 2, 3, 4, 5, and 6)
5. Central limit theorem - mathematical proof and interpretation by simulation;
implications for large sample inference; approximation to Binomial. (Chapter 5)
6. Exact Normal theory: the t and chi-squared distributions. (Chapter 6)
7. Confidence intervals; Interpretation via simulation; Exact results for Normal population mean;
Effect of sample size and choice of confidence level. (Chapter 9)
8. Hypothesis testing; Interpretation via simulation; Exact theory for Normal population mean;
Error types and size of test. (Chapter 9, 14)
9. Theory and examples for paired sample inferences and two-sample inferences. (Ch 11)
10. Analysis of Variance, linear regression, model assessment (through residuals) and interpretation,
hypothesis tests. (Chapters 12, 14) |
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課程目標 |
Introduce the role of statistics in contemporary applications and to develop an elementary understanding of, and fluency in, the statistical paradigm of data collection, exploration, modeling and inference. Inference includes estimation, interval estimation and hypothesis testing.
Both small and large sample theorems of hypothesis testing, interval estimation, and confidence intervals will cover.
It also provides a necessary basis for students for a further study of other advanced statistical courses. |
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課程要求 |
One year Calculus and 機率導論 or equivalent. |
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預期每週課後學習時數 |
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Office Hours |
每週三 13:30~15:30
每週三 10:20~11:20
每週一 14:00~15:00 備註： 週一、週三 授課老師 (天文數學大樓465室) ; 週二2-4PM、週五3-5PM，
助教office hour：週三第56節(天文數學館538室) |
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指定閱讀 |
Rice, J. A. (2007) Mathematical Statistics and Data Analysis. 3rd edition.
Duxbury.
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參考書目 |
References:
1. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Press. (Textbook for
Advanced Statistical Inference)
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Quizzes |
10% |
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2. |
Final |
30% |
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3. |
Midterm |
30% |
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4. |
Homeworks |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/25 |
Monday: Introduction, concepts, notation
Reading: Rice Chapters 1 and 2.1
Wednesday reviews continuous random variables (Rice, Ch 2.2)
Distributions derived from the normal distribution Chapter 2.3) |
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第2週 |
3/02,3/04 |
Monday: Go over EX I in p12 and identify n which maximizes the "likelihood" function of n. Chapters 2.3 and Start with Joint Distribution (Chapter 3.1-3.3)
Wednesday: Go over Proposition C in p13,Independent random variables, Conditional Distribution |
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第3週 |
3/09,3/11 |
Monday: Go over conditional probability in Ch1.5 and show that P(A|B) satisfies 3 axioms required on a probability measure given in p5. Discuss EX D in p24. Read EX E by yourself. Start with Random Variable (Discrete vs Continuous), cdc, pmf, and pdf. Poisson RV, Uniform RV, Normal RV, Function of a RV. Complete Chapter 2. |
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第4週 |
3/16,3/18 |
Cover Rice Chapter 3.1 - 3.6 on joint distribution. |
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第5週 |
3/23,3/25 |
Complete Chapter 3 and Chapter 4.1 to 4.5. |
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第7週 |
4/06,4/08 |
Conditional Expectation and Prediction |
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第9週 |
4/20,4/22 |
Chapter 5 Limit Theorem: Law of Large Numbers, Convergence in Distribution and the Central Limit Theorem |
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第10週 |
4/27,4/29 |
Midterm is given on Monday. It covers the materials from Chapter 1 to Chapter 4.4 and Chapter 5.1 and 5.2. |
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第11週 |
5/04,5/06 |
Convergence in Distribution and the Central Limit Theorem |
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第12週 |
5/11,5/13 |
Chapter 6 Distributions Derived from the Normal Distribution |
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第13週 |
5/18,5/20 |
Chapter 8 Estimation |
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第14週 |
5/25,5/27 |
Monday: Property of MLE such as regularity conditions on the consistency of MLE and asymptotic normality. Wednesday: Quiz 2 (method of estimation) |
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第15週 |
6/01,6/03 |
Chapter 8.7: Efficiency and Cramer-Rao Lower Bound, Confidence Interval, Chapter 9.1 and 9.2 on Neyman-Pearson Paradigm |
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第16週 |
6/08,6/10 |
Ch9.1, 9.2, 9.4, 9.5 Framework of Hypothesis Testing, Likelihood Ratio Test (Refer to the note from p1-14 and textbook.) |
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第17週 |
6/15,6/17 |
Monday: Quiz 3 on hypothesis testing and estimation (Discussion)
Wednesday: Review on homework. |
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