Probability Theory Course Information

Wu: prob112

機率論 (Introduction to Probability Theory)

開課學期：112 學年度第 1、2 學期
開課班級：統計二A
學分數：3/3
上課時間：

星期二第 1, 2 節 (B617)、星期三第 3 節 (B617)
助教實習：星期四第 8, 9 節（蘇建郎助教）

授課老師：

吳碩傑
Office: B831
Tel: 02-2621-5656 ext. 2886
E-mail: shuo@mail.tku.edu.tw
Webpage: https://mail.tku.edu.tw/shuo/

先修科目：微積分

教科書：

Roussas, G. G. (2015). An Introduction to Probability and Statistical Inference, 2nd edition, Academic Press. (Chapters 1 - 6)

推薦參考書籍：

Hogg, R. V., McKean, J. W. and Craig, A. T. (2005). Introduction to Mathematical Statistics, 6th edition, Prentice Hall. (Chapters 1 - 3)
Ross, S. (2009). A First Course in Probability, 8th edition, Prentice Hall.
Roussas, G. G. (1997). A Course in Mathematical Statistics, 2nd ed., Academic Press. (Chapters 1 - 7, 9, 10)

其他參考書籍：

Hoel, P. G., Port, S. C. and Stone, C. J. (1971). Introduction to Probability Theory, Houghton Mifflin Company.
Hogg, R. V. and Craig, A. T. (1995). Introduction to Mathematical Statistics, 5th ed., Prentice Hall. (Chapters 1 - 4)
Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics, 3rd ed., McGraw-Hill. (Chapters I - VI)

主題：

上學期：

Some motivating examples and some fundamental concepts (Sections 1.1, 1.2, Chapter 1)
The concept of probability and basic results (Sections 2.1, 2.3, 2.4, Chapter 2)
Random variables (Section 1.3, Chapter 1)
Distribution of random variable (Section 2.2, Chapter 2)
Expectation, variance and moment generating function (Section 3.1, Chapter 3)
Some probability inequalities (Section 3.2, Chapter 3)
Some special random variables (Section 3.3, Chapter 3)
Median and mode of a random variable (Section 3.4, Chapter 3)

下學期：

Joint p.d.f. and d.f. of two random variables (Sections 4.1, Chapter 4)
Marginal and conditional p.d.f. (Section 4.2, Chapter 4)
Expectation of two random variables, covariance, and correlation coefficient (Section 4.3, Chapter 4)
Generalizations to k random variables (Section 4.4, Chapter 4)
Multinomial, bivariate normal, and multivariate normal distributions (Section 4.5, Chapter 4)
Independence of random variables and some applications (Chapter 5)
Transformation of random variables (Sections 6.1, 6.2, 6.4, Chapter 6)
Order statistics (Section 6.5, Chapter 6)
Linear transformations (Section 6.3, Chapter 6; time permitting)

評分方法：

助教實習： 25% （凡修本課程者一律必須上實習課，否則助教實習分數以零分計算）
複習考： 10% （開學第二週於助教實習課舉行，未參加者以零分計算，不接受補考。若第二週遇國定假日，則提前至第一週舉行）
期中考： 30%
期末考： 35%
第 1 學期：
- 本課程沒有點名分數，也沒有任何點名加分機制，請不要有無缺課就會及格或不擋修的想法！
第 2 學期：
- 全學期不點名，不想上課也不用請假，反正就是不點名了！
- 學期成績就是按照上述百分比來計算，不要期待點名加分。

練習作業：

Section 1.2	2.1, 2.3, 2.4, 2.6, 2.7, 2.9, 2.12, 2.13, 2.14, 2.15, 2.16
Section 2.1	1.2, 1.3, 1.4, 1.6, 1.7, 1.8, 1.9(i), 1.11, 1.12, 1.13, 1.14
Section 2.3	3.2, 3.4, 3.5, 3.6, 3.7, 3.9, 3.11, 3.12, 3.13, 3.14, 3.16, 3.18, 3.19, 3.21, 3.23, 3.24, 3.25, 3.28, 3.29, 3.32, 3.37
Section 2.4	4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.9, 4.12, 4.13, 4.14, 4.17, 4.18
Section 2.5	5.9, 5.10, 5.11, 5.12, 5.13
Section 1.3	3.1, 3.4, 3.6, 3.8
Section 2.2	2.2, 2.3, 2.4, 2.5, 2.7, 2.8, 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, 2.19, 2.20, 2.21, 2.23
Section 3.1	1.2, 1.3, 1.6, 1.8, 1.9, 1.11, 1.12, 1.13, 1.14, 1.15, 1.17, 1.20, 1.21, 1.28, 1.29, 1.30, 1.31, 1.33, 1.36, 1.41, 1.42, 1.46, 1.48, 1.49, 1.50, 1.52, 1.53
Section 3.2	2.1, 2.2, 2.3, 2.4
Section 3.3	3.1, 3.2, 3.3, 3.5, 3.7, 3.8, 3.9, 3.12, 3.13, 3.15, 3.18, 3.19, 3.20, 3.25, 3.26, 3.30, 3.31, 3.32, 3.33, 3.34, 3.35, 3.36, 3.38, 3.40, 3.42, 3.43, 3.48, 3.49, 3.50, 3.52, 3.55, 3.56, 3.60, 3.61, 3.67, 3.68, 3.70, 3.72, 3.75, 3.76, 3.84, 3.85, 3.88
Section 3.4	4.1, 4.3, 4.4, 4.7, 4.10, 4.12, 4.13, 4.15
Section 4.1	1.2, 1.3, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11
Section 4.2	2.4, 2.5, 2.6, 2.9, 2.10, 2.11, 2.15, 2.18(ii) (iii), 2.19, 2.23, 2.24, 2.25, 2.27, 2.28, 2.29, 2.30, 2.31, 2.34, 2.37, 2.39
Section 4.3	3.4, 3.8, 3.10, 3.13, 3.14, 3.15, 3.16, 3.18, 3.21, 3.23
Section 4.4	4.1, 4.2, 4.4
Section 4.5	5.2, 5.4, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12, 5.13, 5.19, 5.20, 5.21
Section 5.1	1.3, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.13, 1.14, 1.15, 1.20, 1.22, 1.23, 1.29, 1.33, 1.34, 1.36
Section 5.2	2.1, 2.3, 2.4, 2.6, 2.8, 2.10, 2.11, 2.12, 2.13, 2.16
Section 6.1	1.1, 1.3, 1.4, 1.5, 1.6, 1.7, 1.10, 1.11
Section 6.2	2.2, 2.3, 2.5, 2.6, 2.7, 2.9, 2.11, 2.12, 2.14, 2.15
Section 6.4	4.1
Section 6.5	5.1, 5.4, 5.5, 5.6, 5.7, 5.12, 5.15
Section 6.3	3.3, 3.6, 3.7

Last modified: 7:23:32 Saturday January 13, 2024 by Shuo-Jye Wu