課程資訊
課程名稱
機率導論
INTRODUCTION TO PROBABILITY THEORY 
開課學期
98-1 
授課對象
理學院  數學系  
授課教師
謝南瑞 
課號
MATH2501 
課程識別碼
201 31700 
班次
 
學分
全/半年
半年 
必/選修
必修 
上課時間
星期二5,6(12:20~14:10)星期四5,6(12:20~14:10) 
上課地點
新302新302 
備註
1.學士班三年級必修課。 2.內容含馬可夫鏈與泊松過程導論。
限本系所學生(含輔系、雙修生)
總人數上限:60人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/981ele_probab 
課程簡介影片
 
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課程大綱
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課程概述

1. Random events and Probability: counting, operations, probability space, urn problem, etc
2. Conditional Probability: conditioning, independence, formulae, Baysian, etc.
3. Random Variables and Distributions : rv and distribution function, discrete-type rv , continuous-type rv, joint (multivariate)- type rv, sum and max of i.i.d. rv’s, conditional-type rv, etc
4. Expectation, Variance, and other Macro-values: expected value, formulae, variance and covariance, correlation, conditional expectation, moment generating function, etc
5. Limits Theorems: some inequalities (Markov, Chebyshev, Chernoff, Cauchy-Schwarz), law of large numbers, DeMoirve-Laplace Theorem, Central Limit Theorem, Poisson Limit Theorem, Approximation of binomial distribution, etc.
6. Poisson Process: inter-arrival and waiting times, Poisson v.s. exponential distributions, compound Poisson process(optional)
7. Finite-state Markov Chain: Random walk, Markov property, Markov matrix, Chapman-Kolmogorov equation, state-classification, invariant distribution, continuous-time MC ( the last three are optional)
 

課程目標
To be familiar with basic probability and stochastic process, toward interest in random phenomena. 
課程要求
Course prerequisite:
Calculus, Linear algebra, and some Ordinary Differential Equations (for 6 and 7, optional)

Grading scheme:
Mid-term: 1-4 of the content, 40 %
Final: 4-7 of the content, 40 %
Homework, 20%
 
預期每週課後學習時數
 
Office Hours
每週二 15:30~17:30 
指定閱讀
Lecture Notes by N.-R. Shieh 
參考書目
Lecture Notes by N.-R. Shieh
(the 2009 version is in CEIBA for registered students; old version in personal
homepage)
R. Durrett: The Essentials of Probability
R. Durrett: Essentials of Stochastic Processes (Chapters 1 and 3)
S. Ross: A First Course in Probability, the 5th or newer Edition (the newest is the 8th).
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Mid-term: 1-4 of the content 
40% 
 
2. 
Final: 4-7 of the content,  
40% 
 
3. 
Homework, Quiz  
20% 
 
 
課程進度
週次
日期
單元主題
第3週
9/29,10/01  Quiz 1 
第5週
10/13,10/15  Quiz 2 
第7週
10/27,10/29  Quiz 3 
第9週
11/10,11/12  Mid-term exam at 11/12 
第12週
12/01,12/03  Quiz 4 
第14週
12/15,12/17  Quiz 5 
第16週
12/29,12/31  Quiz 6 
第1-17週
2009/09/14--2010/01/08  Lecture Notes by N.-R. Shieh
(the 2009 version is in CEIBA for registered students,
will post from 2009/09/01).
Reference answers for homework 
第2-18週
2009/09/22-2010/01/15  Special homework to non-math students