Mathematical Statistics II

Spring 2025

Course Info ～歡迎來到由 YES 主持的數理統計學課程網站～

Syllabus

Lectures: M. 1300-1400, R. 1300-1500 @ SE A210

Instructor: Yu-Ling Tseng.

Office Hours: T. 1200~1300 R. 1500~1600@SE A409

Prerequisites: Probability Theory, Statistics

TA: 蔡念秤 M. 15:00~16:00 @ SE 412 吳雨瑾 T. 11:00~12:00 @ SE B302

～有問題要多多請教助教喔

數學小天地 ～～討論各類數學相關問題的好地方～～

Class Notes

期末考訂於0612（星期四）12：30～15：00舉行。。。。。。。。
考試範圍：信賴集合估計（所以有時檢定結果會用到）
同學可以攜帶計算機應考（也許會用到？）

號外～～～～
今年獨有的加分機會！！來囉～～～！

6/18早上（確切時間系上近期會公告）有個統計中研院院士來系上演講，鼓勵同學參加～～～
所以，來聽演講時和Yes簽到的迴歸、數統修課同學學期分數加10分（不適用要拿A+的）。（哇～加很大耶，該把握的要把握呀：））

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學期只有 17 周上課時間，學校行事曆18周的彈性補課。。。。。

我們就

星期一、四都 13 點整開始上課～～大家一起加油喔～

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數統（－）期末考考題

Solution

********

考試時，若同學需要，會提供以下密度函數表供同學參考

密度函數表

0424（R）期中考成績枝葉圖

總分：120 修課/ 應考人數：38/33

0 | 555999
1 | 13567
2 | 24567
3 | 14557
4 | 178
5 | 024
6 | 8
7 |
8 |
9 | 3
10 | 1379

Q1: 15 Q2: 31 Q3: 50

Mean: 38.88 s.d.: 31.75

以上，不計缺考

註：成績顏色帶代表：紅色是警告區，黃色是小心後通行區，綠色是安全通行區

（就像紅綠燈號誌呀）

Assignments (No late homework is allowed.)

Date	Hand-in Problems	Due Date
0529	12.7 #1 (i, iii), 2, (i, iii), 3 (i, iii, iv), 4 (iii) 12.8 #1	這份作業不用交。但，同學一定要自己做過這些題目喔
0522	15.4. 1, 2 Problem on consistency: 1. Consider a population of finite mean u and finite variance, show that a UMVUE, if exists, for u is always consistent; 2. Show that the sample variance is always consistent for the population variance, if it exists. Also, give three different consistent estimators for the population variance. (4 problems in total)	0529
0515	15.2. # 1, 2, 3, 5, 6, 8, 9, 10 15.3. # 1 (9 problems in total)	0522
0508	Probelms are given here.	0515
0417	13.8 #4, 7, 9 13.8 #5, 8 and Question: It is often assumned that scores of a course are normally distributed. Test this claim for our MathStat(2) midterm #1 (20210513) data, at level 0.05. FYI: R to do GOF with one mathstat1 midterm where average score is 35.93 s.d. s=27.	0424 期中考，這份作業請練習但不用交。 More ex on contingency table
0410	13.5. #1, 2 (use the equal-tailed test) , 3, 4, 5 13.6. #1, 2, 4, 5, 7 (Use the equal-tailed test for problem 1, 2) (10 problems in total)	0417
0327	13.4. #2 # 1, 2, 3, 4 given in Problems , and 13.7. #1 (i, ii, iii), 3 (7 problems in total)	0410
0320	13.3. # 7, 8, 9, 10 （注意：這些題目有些部份是要同學練習利用CLT求得檢定或求特定power要求下的樣本數。。。。。。。以後，除非題目要求用CLT，所有數統MP/UMP/UMPU題目都要以題目所給的密度函數做喔） (4 problems in total)	0327
0313	13.2. #2 13.3. #1, 2, 4, 5, 6, 12 (7 problems in total)	0320
0306	Problems given here and 13.2 #1,4, 5, 6, 7. (9 problems in total)	0313
0227	Problems are given here.	0306

20250217 First day of class

Textbook: A course in mathematical statistics. 2/e By G. G. Roussas

Reference: Statistical Inference. By Casella and Berger (1990, 2002)

Course Grade

Homework (10%) Midterms (45%) Final (45%)

References

Roussas, G. G. (1997). A Course in Mathematical Statistics 2/e. San Diego, CA: Academic Press. (Textbook).
Casella, G. and Berger,"R. L. (1990). Statistical Inference. Pacific Drove, CA: Wadsworth.
Rohatgi, V. K. (1976). An Introduction to Probability Theory and Mathematical Statistics, Wiley and Sons.
Lehmann, E. L. (1991). Theory of point estimation. Pacific Grove, Calif.: Wadsworth & Brooks/Cole.

統計之路

Last modified: 050715
yltseng@mail.ndhu.edu.tw