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課程名稱 |
機率導論
INTRODUCTION TO PROBABILITY THEORY |
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開課學期 |
95-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳 宏 |
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課號 |
MATH2501 |
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課程識別碼 |
201 31700 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期二5,6(12:20~14:10)星期三5,6(12:20~14:10) |
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上課地點 |
新生505 |
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備註 |
總人數上限：100人
外系人數限制：25人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/951IntroProb |
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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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. Basics
2. Conditional Probability: It includes independence, conditional probability,
and Bayes formula.
3. Distributions: It includes asymptotic approximation such as Poisson
approximation to Binomial, density and distribution functions, joint
distributions, marginal distributions, independence, and conditional
distributions
4. Expected Value: It includes moments, generating functions, expectation,
variance and covariance, correlation, and conditional expectation.
5. Limit Theorems: It includes laws of large numbers, the central limit theorem,
confidence intervals, and hypothesis testing. |
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課程目標 |
Probability is the language in which to study chance phenomena, and whose
concepts are fundamental to many diverse fields including physics, economics
and statistics. The objective of this course is to provide students having
a good calculus background with a solid mathematical treatment of the fundamental
concepts and techniques of probability theory. It is fundamentally important
for understanding the commonly observed random phenomena. |
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課程要求 |
Prerequist: Calculus and one-semester linear algebra |
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預期每週課後學習時數 |
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Office Hours |
每週三 15:10~16:00
每週二 15:20~16:20 備註： If it does not fit to your schedule, please write email to me to set
up appointment. |
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指定閱讀 |
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參考書目 |
教科書:
R. Durrett: The Essentials of Probability, Duxbury Press 1994 |
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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. |
Final Exam |
35% |
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2. |
Midterm Exam |
30% |
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3. |
Quizzes |
20% |
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4. |
Homework |
15% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/19,9/20 |
1.1: Experiments and Events;
1.2: Probabilities;
1.4: Urn Problems
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第2週 |
9/26,9/27 |
1.5: Repeated Experiments;
1.6: Probabilities;
Review of Homework |
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第3週 |
10/03,10/04 |
緩衝時間
2.1: Independence;
Review of Homework;
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第4週 |
10/11 |
2.2: Conditional Probability;
2.3: Two-Stage Experiments
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第5週 |
10/17,10/18 |
2.4: Bayes Formula;
Review of Homework;
2.5: Recursion |
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第6週 |
10/24,10/25 |
2.5: Recursion;
3.1: Poisson Approximation;
Quiz 1 |
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第7週 |
10/31,11/01 |
3.2: Density and Distribution Functions;
3.3: Functions of Random Variables;
Quiz 2;
3.4: Joint distributions
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第8週 |
11/07,11/08 |
3.5: Marginal Distributions & Independence;
3.6: Functions of Several Random Variables;
Quiz 2
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第9週 |
11/14,11/15 |
Midterm;
3.7: Sums of independent random variables |
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第10週 |
11/21,11/22 |
4.1: Expectation;
4.2: Generating functions;
Review of Homework
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第11週 |
11/28,11/29 |
4.3: Properties of expectation;
緩衝時間;
Review of Homework
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第12週 |
12/05,12/06 |
4.4: Variance and Covariance;
4.5: Conditional Expectation;
Review of Homework |
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第13週 |
12/12,12/13 |
4.5: Conditional Expectation;
Quiz 3;
5.1: Law of Large Numbers
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第14週 |
12/19,12/20 |
5.1: Law of Large Numbers;
5.2: Central Limit Theorem;
Review of Homework |
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第15週 |
12/26,12/27 |
緩衝時間;
Quiz 4;
5.3: Confidence Intervals |
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第16週 |
1/02,1/05 |
Review;
5.3: Confidence Intervals;
Review of Homework |
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第17週 |
1/09,1/10 |
5.4: Hypothesis Testing;
Review |
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第18週 |
1/16 |
Final Exam |
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