SDST7610 Probability Theory (6 credits) Academic Year 2026
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 Status with Related Major/Minor /Professional Core 2U000C00 Course not offered under any Major/Minor/Professional core
2026 Professional Core in Risk Management ( Disciplinary Elective )
2026 Professional Core in Statistics ( Disciplinary Elective )
2025 Professional Core in Risk Management ( Disciplinary Elective )
2025 Professional Core in Statistics ( Disciplinary Elective )
Course to PLO Mapping 2026 Professional Core in Risk Management < PLO 2,3,6 >
2026 Professional Core in Statistics < PLO 2,4,6 >
2025 Professional Core in Risk Management < PLO 2,3,6 >
2025 Professional Core in Statistics < PLO 2,4,6 >
Offer in 2026 - 2027 Y        2nd sem    Examination May     
Offer in 2027 - 2028 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