課程資訊

Introduction to Probability Theory

106-2

MATH2502

201 49740

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1062MATH2502_

Contents : Axioms of probability, conditional probability, independence, random variables, jointly distributed random variables, expectation, moment generating functions, limit theorems, Poisson processes, Markov chains.

Probability theory, originated in the consideration of games of chance, is the language to study commonly observed random phenomena. It has become a fundamental tool used by nearly all scientists, including engineers, economists, industrialists, social scientists, medical practitioners, physicists, statisticians, etc. The main objective of this course is to provide students, who possess the prerequisite calculus background, with a solid mathematical
treatment of the fundamental concepts and techniques of probability theory. Another goal is to demonstrate the many diverse possible applications of the subject through many examples.

https://en.wikipedia.org/wiki/Probability_axioms
then email the instructor

Homework set 8-10題, 小考從裡面出2-4題;

Office Hours

Richard Durrett : The Essentials of Probability 1994
Sheldon Ross : A First Course in Probability 2012 9th edition
Grinstead and Snell : Introduction to Probability 2006 2nd
H. Pishro-Nik : Introduction to Probability, Statistics and random processes (Free online textbook) https://www.probabilitycourse.com/

For Poisson processes, lecture note.

For Markov chains,
Ch 11 in Grinstead and Snell’s Introduction to Probability 2006 2nd (Free probability ebook)
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf

(僅供參考)

 No. 項目 百分比 說明 1. Quizzes 15% 6 quizzes, drop the lowest one. 2. Midterm 35% 3. Final 40% 4. Homeworks 5% 5. class participation 5%

 課程進度
 週次 日期 單元主題 第1週 2/27,3/01 Introduction; Ch 2 Rules of probability 2.1-2.5 2.5-7 第2週 3/06,3/08 Ch 2 Rules of probability 2.7-9; Recitation; 2.9-13 第3週 3/13,3/15 Ch 3 Counting and gambling 3.1-10 Recitation HW1 due ; HW1 ch2 #5,10,14,15,19,20,26,31 Grinstead and Snell 4.1 #1-5a, 55,56,58,60 第4週 3/20,3/22 Ch 4 Distributions 4.1-8; Recitation Quiz 1(HW1), HW 2 due ch3 ex 9.1 problem #4,7,14,15,16,19,20, 3-state; 第5週 3/27,3/29 Ch 5 Random variables 5.1-6 Recitation Quiz 2 (HW 2); 第6週 4/03,4/05 Holidays 第7週 4/10,4/12 Ch 5 Random variables inequalities, 5.8-9 Recitation HW 3 due ch4 ex 9.1, Poisson to normal, 11.1, 11.2, 12.1 #9,10,11,12,25 第8週 4/17,4/19 Ch 6 Jointly 6.2-3; Polya urn model, random permutation, convergence in distributions Recitation Quiz 3 HW 4 due ch5 #4,6,10,11,15,16,20a,23b,27,28,31 第9週 4/24,4/26 6.4 6.7 Review Midterm (Ch 2,3,4,5,6.2, Applications) 第10週 5/01,5/03 自主學習周; Ch6 6.5-8 第11週 5/08,5/10 Ch 6 Jointly 6.9-10; 6.11 Recitation 檢討期中 第12週 5/15,5/17 6.12-13,Law of large numbers, Borel-Cantelli lemma; Recitation HW5 due Ch6 ex 3.1, 4.3 # 1,3,10,12,15,19,21,22 第13週 5/22,5/24 Momemt generating functions; Central limit theorems Recitation Quiz 4(HW 5); HW6 due Ch 6 ex12.1,13.1bc #4,28,31,32,42 +SLLN*3 第14週 5/29,5/31 Branching processes, 11.1 Markov Chains ; Recitation Quiz 5(HW 6) 第15週 6/05,6/07 no class on 6/5; 11.2 Absorbing MC 第16週 6/12,6/14 11.3 Regular MC,Poisson processes; Recitation Quiz 6(HW 7) #4,8,9,12,15,20, notes*4 第17週 6/19,6/21 Review ; 6/21 Final (Ch 6, SLLN, Ch 7, Markov Chains, Poisson processes)