課程資訊

INTRODUCTION TO PROBABILITY THEORY

95-1

MATH2501

201 31700

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/951IntroProb

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.

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.

Prerequist: Calculus and one-semester linear algebra

Office Hours

R. Durrett: The Essentials of Probability, Duxbury Press 1994

(僅供參考)

 No. 項目 百分比 說明 1. Final Exam 35% 2. Midterm Exam 30% 3. Quizzes 20% 4. Homework 15%

 課程進度
 週次 日期 單元主題 第1週 9/19,9/20 1.1: Experiments and Events; 1.2: Probabilities; 1.4: Urn Problems 第2週 9/26,9/27 1.5: Repeated Experiments; 1.6: Probabilities; Review of Homework 第3週 10/03,10/04 緩衝時間 2.1: Independence; Review of Homework; 第4週 10/11 2.2: Conditional Probability; 2.3: Two-Stage Experiments 第5週 10/17,10/18 2.4: Bayes Formula; Review of Homework; 2.5: Recursion 第6週 10/24,10/25 2.5: Recursion; 3.1: Poisson Approximation; Quiz 1 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 第8週 11/07,11/08 3.5: Marginal Distributions & Independence; 3.6: Functions of Several Random Variables; Quiz 2 第9週 11/14,11/15 Midterm; 3.7: Sums of independent random variables 第10週 11/21,11/22 4.1: Expectation; 4.2: Generating functions; Review of Homework 第11週 11/28,11/29 4.3: Properties of expectation; 緩衝時間; Review of Homework 第12週 12/05,12/06 4.4: Variance and Covariance; 4.5: Conditional Expectation; Review of Homework 第13週 12/12,12/13 4.5: Conditional Expectation; Quiz 3; 5.1: Law of Large Numbers 第14週 12/19,12/20 5.1: Law of Large Numbers; 5.2: Central Limit Theorem; Review of Homework 第15週 12/26,12/27 緩衝時間; Quiz 4; 5.3: Confidence Intervals 第16週 1/02,1/05 Review; 5.3: Confidence Intervals; Review of Homework 第17週 1/09,1/10 5.4: Hypothesis Testing; Review 第18週 1/16 Final Exam