Download advanced probability theory

Department of Statistics
Graduate Program
R270500
Advanced Probability Theory
(高等機率論)
Fall 2010
The mission of the Department of Statistics is to cultivate quality professionals with enthusiasm
and global perspectives.
Graduate Program Learning Goals (goals covered by this course are indicated):

1
Graduate students should be able to communicate effectively verbally and in writing.

2
Graduate students should solve strategic problems with a creative and innovative approach.
3
Graduate students should demonstrate leadership skills demanded of a person in authority.
4
Graduate students should possess a global economic and management perspective.
5
Graduate students should possess the necessary skills and values demanded of a true professional.

Instructor/開課教師:
Ray-Bing Chen /陳瑞彬
Prerequisite/先修科目 :
Elementary Probability Theory、Calculus
Course Description/課程概述:
The course shall starts with set theory in which concept of  -algebra and probability space
further follows. Random phenomena will be discussed and linked to all various types of
random variables of random vectors in both discrete and continuous cases. Then random
sequences and will-known stochastic processes shall be introduced with discussions on
related limit situations, local behaviors, together with required computational techniques.
Course Objectives/教學目標:
Teach students the concept of probability in relation to randomness occurring in all sorts of
phenomena. Then methods shall be taught to enable the students on how to manipulate the
randomness concept for practical applications.
Content Summary/授課課程大綱明細:
1. Construction of measures on  -fields.
2. Probability spaces and random variables.
3. Probability distributions.
4. Probability laws and types of laws.
5. Charosteristic functions of extensions.
6. Central limit problem and solutions.
7. Variois discrete and continuous random processes.
Textbook/教材課本:
1. Probability and Measure, 3rd Edition, by P. Billingsley, Wiley-Interscience (1995).
2. A Course in Large Sample Theory, by T. S. Ferguson, Chapman & Hall/CRC Texts in
Statistical Science (1996).
Recommended references/參考書目:
1. A Course in Probability Theory, 2nd Edition, by K. L. Chung, Academic Press (2000).
2. Introduction to Probability Models, 10th Edition, by S. M. Ross, Academic Press
(2009).
Course Requirement/課程要求:
Grading Policy/評量方式:
1. HW 30%
2. Midterms 35%
3. Final 35%
Grading Policy for AACSB Multiple Assessment:
HW Midterms
30%
35%
 Oral Commu./ Presentation
COMMU
 Written Communication
30%
30%
 Creativity and Innovation
 Problem Solving
30%
30%
CPSI
 Analytical &
20%
20%
Computational Skills
 Leadership & Ethic
LEAD
 Social responsibility
GLOB
 Global Awareness
VSP
 Values, Skills & Profess.
 Information Technology
 Management Skills
10%
10%
10%
10%
Final
35%
30%
30%
20%
10%
10%