課程資訊

Introduction to Probability Theory

99-2

MATH2501

201 31700

02

1.學士班二年級必修課。2.內容含馬可夫鏈與泊松過程導論。(此班99學年加開，給大三學生修)

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/992IntrProb

Probability space, conditional probability and independence, discrete and continuous random variables and random vectors, (joint, conditional) distributions, (conditional) expectations and variances, generating functions, and a brief introduction of limit theorems, Poisson process, and Markov chains.

Calculus and basic matrix theory.

Office Hours

Text:
Introduction to Probability by D. P. Bertsekas and J. N. Tsitsiklis, 2nd edition, 2008, Athena Scientific.

References:
1. Introduction to Probability by Charles Grinstead and Laurie Snell. Visit the website http://www.dartmouth.edu/~chance for download.
2. A First Course in Probability by Sheldon Ross, Prentice Hall.

(僅供參考)

 No. 項目 百分比 說明 1. Exam 1 20% 2. Exam 2 20% 3. Final 30% 4. Homework 20% 5. Recitation 10%

 課程進度
 週次 日期 單元主題 第1週 2/21,2/23 Definition and examples of (discrete and continuous) Probability space, conditional probability, total probability theorem and Bayes' rule (1.1-1.4) 第2週 2/28,3/02 Independence (1.5) 第3週 3/07,3/09 Basic concepts of discrete and general random variables, probability mass and distribution functions, expectations, mean, variance, and important discrete random variables (2.1-2.4) 第4週 3/14,3/16 Random vectors, conditioning, and independence (2.5 - 2.8) 第5週 3/21,3/23 Continuous random variables, density functions, distribution functions, and important examples. Jointly continuous random vectors (3.1 - 3.4) 第6週 3/28,3/30 Conditioning and independence (3.5). The continuous Bayes' rule (3.6) is skipped 第7週 4/04,4/06 No class 第8週 4/11,4/13 Derived distributions (4.1). Exam 1 (04/13) on Chapters 1, 2, and 3 (except 3.6). 第9週 4/18,4/20 Covariance and correlation, conditional expectation and variance revisited, moment generating functions, and sum of a random number of independent random variables (4.2 - 4.5) 第10週 4/25,4/27 Modes of convergence, Markov and Chebyshev inequalities, L^2 and L^1 weak laws of large numbers, almost sure convergence and Borel-Cantelli lemma (5.1, 5.2, 5.3, 5.5) 第11週 5/02,5/04 Relations among various modes of convergence, strong law of large numbers, Levy continuity theorem, central limit theorem, and examples (5.4, 5.5) 第12週 5/09,5/11 Introduction to and examples of Markov chains, Chapman-Kolmogorov equation, and classification of states 第13週 5/16,5/18 Recitation on 05/16, and an Exam 2 about Chapters 4 and 5 on 05/18 第14週 5/23,5/25 Strong Markov property, classification of states, limit behaviors, and absorbing Markov chains (notes and 11.2 of G-S) 第15週 5/30,6/01 Regular and irreducible Markov chains (11.3 of G-S) 第16週 6/06,6/08 Mean first passage and recurrence times (11.5 of G-S) 第17週 6/13,6/15 Fundamental matrix of an irreducible Markov chain and some discussions of exercises. Recitation on 06/15. Final exam: 10:10 - 12:10 of 06/22