SemesterFall Semester, 2025
DepartmentPhD Program of Statistics, First Year PhD Program of Statistics, Second Year
Course NameTheory of Probability
InstructorWENG CHIU-HSING
Credit3.0
Course TypeRequired
Prerequisite
Course Objective
Course Description
Course Schedule

Weekly class schedule (tentative):



   「課程主題」                                                                                 「課程內容與指定閱讀」 「教學活動與作業」

1. The weak law of large numbers, the strong law of large numbers        section 1                     in-class exercise 

2. Probability measures, Lebesgue measure on the unit interval              section 2                     homework 1

3. measurable sets, nonmeasurable sets                                                  section 4                     in-class exercise

4. Denumerable probabilities, limit sets, Borel-Cantelli lemmas                section 4                     homework 2

5. Simple random variables                                                                        section 5                     in-class exercise

6. The law of large numbers revisit                                                             section 6                    homework 3

7. Markov Chains, Chernoff's theorem                                                        section 8                    in-class exericse

8. The law of the iterated logarithm, measurable functions                         seciont 9                    homework 4

9. midterm                       

10. Distribution functions, weak convergence                                              section 12                 in-class exercise

11. Integral, Integration to the limit, uniform integrability                              section 13                 homework 5

12. Integral with respect to Lebesgue measure                                           section 15                 in class exercise

13. Product measure and Fubini theorem                                                    section 16                 homework 6

14. Convergence of distributions                                                                  section 17                 in-class exercise

15. Conditional expectation and martingales                                               section  30                 homework 7

16. final exam


Teaching Methods
Teaching Assistant

TBA


Requirement/Grading

Grading policy:

homework + presentation 50%

midterm   25%

final     25%

 


Textbook & Reference

Probability and Measure, (3rd ed. Wiley) by Patrick Billingsley

Stochastic Processes, (2nd ed. Wiley) by Sheldon Ross


Urls about Course
Attachment