| Academic Year |
2025 |
| Offering Department |
SCDS (Department of Statistics and Actuarial Science) |
Quota |
---
|
| Course Co-ordinator |
Prof M Hofert, SCDS (Department of Statistics and Actuarial Science) < mhofert@hku.hk > |
| Teachers Involved |
(Prof M Hofert,Statistics & Actuarial Science) |
| Course Objectives |
This course provides an introduction to measure theory and probability. The course will focus on some basic concepts in theoretical probability which are important for students to do research in actuarial science, probability and statistics. |
| Course Contents & Topics |
Contents include: sigma-algebra, measurable space, measure and probability, measure space and probability space, measurable functions, random variables, integration theory, characteristic functions, convergence of random variables, Hilbert spaces, conditional expectation, martingales. |
| Course Learning Outcomes |
On successful completion of this course, students should be able to:
| CLO 1 |
understand the fundamental measure theory and probability theory |
| CLO 2 |
learn the general concept of integration, understand the monotone convergence theorem, Fatou's lemma and dominated convergence theorem |
| CLO 3 |
understand the concept of conditional expectation |
| CLO 4 |
have some elementary knowledge of martingale |
|
Pre-requisites
(and Co-requisites and
Impermissible combinations) |
Pass in SDST3603 or SDST3903
Only for students admitted in 2025 and thereafter. |
| Course to PLO Mapping |
|
| Offer in 2025 - 2026 |
Y
2nd sem
|
Examination |
May
|
| Offer in 2026 - 2027 |
Y |
| Course Grade |
A+ to F
|
| Grade Descriptors |
| A | Demonstrate thorough mastery at an advanced level of extensive knowledge and skills required for attaining all the course learning outcomes. Show strong analytical and critical abilities and logical thinking, with evidence of original thought, and ability to apply knowledge to a wide range of complex, familiar and unfamiliar situations. Apply highly effective organizational and presentational skills. |
|---|
| B | Demonstrate substantial command of a broad range of knowledge and skills required for attaining at least most of the course learning outcomes. Show evidence of analytical and critical abilities and logical thinking, and ability to apply knowledge to familiar and some unfamiliar situations. Apply effective organizational and presentational skills. |
|---|
| C | Demonstrate general but incomplete command of knowledge and skills required for attaining most of the course learning outcomes. Show evidence of some analytical and critical abilities and logical thinking, and ability to apply knowledge to most familiar situations. Apply moderately effective organizational and presentational skills. |
|---|
| D | Demonstrate partial but limited command of knowledge and skills required for attaining some of the course learning outcomes. Show evidence of some coherent and logical thinking, but with limited analytical and critical abilities. Show limited ability to apply knowledge to solve problems. Apply limited or barely effective organizational and presentational skills. |
|---|
| Fail | Demonstrate little or no evidence of command of knowledge and skills required for attaining the course learning outcomes. Lack of analytical and critical abilities, logical and coherent thinking. Show very little or no ability to apply knowledge to solve problems. Organization and presentational skills are minimally effective or ineffective. |
|---|
|
| Communication-intensive Course |
N |
| Course Type |
Lecture-based course |
Course Teaching
& Learning Activities |
| Activities |
Details |
No. of Hours |
| Lectures |
|
36.0 |
| Tutorials |
|
12.0 |
| Reading / Self study |
|
100.0 |
|
Assessment Methods
and Weighting |
| Methods |
Details |
Weighting in final
course grade (%) |
Assessment Methods
to CLO Mapping |
| Assignments |
Coursework (assignments, tutorials, and a class test) |
40.0 |
1,2,3,4 |
| Examination |
One 2-hour written examination |
60.0 |
1,2,3,4 |
|
Required/recommended reading
and online materials |
Jean Jacod and Philip Protter: Probability Essentials (Universitext, Springer-Verlag,
New York, 2004, 2nd edition)
Chung K. L.: A Course in Probability Theory (Academic Press, 2001, 3rd edition) |
| Course Website |
http://moodle.hku.hk |
| Additional Course Information |
NIL |