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課程名稱 |
機率導論
Introduction to Probability Theory |
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開課學期 |
99-2 |
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授課對象 |
數學系 |
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授課教師 |
張志中 |
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課號 |
MATH2501 |
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課程識別碼 |
201 31700 |
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班次 |
02 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期一3,4(10:20~12:10)星期三3,4(10:20~12:10) |
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上課地點 |
天數102天數204 |
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備註 |
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)
總人數上限：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/992IntrProb |
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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 |
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. |
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課程目標 |
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課程要求 |
Calculus and basic matrix theory. |
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預期每週課後學習時數 |
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Office Hours |
備註： |
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指定閱讀 |
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參考書目 |
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. |
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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. |
Exam 1 |
20% |
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2. |
Exam 2 |
20% |
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3. |
Final |
30% |
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4. |
Homework |
20% |
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5. |
Recitation |
10% |
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週次 |
日期 |
單元主題 |
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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) |
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第2週 |
2/28,3/02 |
Independence (1.5) |
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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) |
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第4週 |
3/14,3/16 |
Random vectors, conditioning, and independence (2.5 - 2.8) |
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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) |
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第6週 |
3/28,3/30 |
Conditioning and independence (3.5). The continuous Bayes' rule (3.6) is skipped |
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第7週 |
4/04,4/06 |
No class |
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第8週 |
4/11,4/13 |
Derived distributions (4.1). Exam 1 (04/13) on Chapters 1, 2, and 3 (except 3.6). |
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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) |
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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) |
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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) |
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第12週 |
5/09,5/11 |
Introduction to and examples of Markov chains, Chapman-Kolmogorov equation, and classification of states |
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第13週 |
5/16,5/18 |
Recitation on 05/16, and an Exam 2 about Chapters 4 and 5 on 05/18 |
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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) |
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第15週 |
5/30,6/01 |
Regular and irreducible Markov chains (11.3 of G-S) |
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第16週 |
6/06,6/08 |
Mean first passage and recurrence times (11.5 of G-S) |
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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 |
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