Enquiry for Science Major/Minor/Programme Requirements
MATH3603 Probability theory (6 credits) Academic Year 2025
Offering Department Mathematics Quota ---
Course Co-ordinator Prof Z Bao, Mathematics < zgbao@hku.hk >
Teachers Involved (Prof Z Bao,Mathematics)
Course Objectives The emphasis of this course will be on probability models and their applications. The primary aim is to elucidate the fundamental principles of probability theory through examples and to develop the ability of the students to apply what they have learned from this course to widely divergent concrete problems.
Course Contents & Topics -Basic probability theory: random variable, discrete and continuous probability distributions, expectation, variance, moment generating function, strong law of large numbers, central limit theorem.
-Conditional probability theory: conditional probability, Bayes theorem, conditional expectation, conditional variance, compound random variable, Polya's urn model, Bose-Einstein statistics.
-Markov chain theory: concepts of states and transition probability, irreducibility, stationary distribution, limiting probabilities, reversibility, hidden Markov chain, applications in marketing and genetic problems, branching process, Markov decision process.
-Poisson process and reliability theory: exponential distribution, memoryless property, Poisson process, concepts of reliability, applications to server queue problems.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 understand and recognize the fundamental principles of probability theory
CLO 2 explain the typical proofs and computational techniques in probability theory and apply them to concrete problems
CLO 3 demonstrate knowledge and understanding of various types of probability models
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in (MATH2101 and MATH2211) or MATH2014 or (MATH1821 and MATH2822)
Course Status with Related Major/Minor /Professional Core 2025 Major in Mathematics ( Disciplinary Elective )
2025 Major in Mathematics (Intensive) ( Core/Compulsory )
2025 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2025 Minor in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics (Intensive) ( Core/Compulsory )
2024 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2024 Minor in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics (Intensive) ( Core/Compulsory )
2023 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2023 Minor in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics (Intensive) ( Core/Compulsory )
2022 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2022 Minor in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics (Intensive) ( Core/Compulsory )
2021 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping 2025 Major in Mathematics < PLO 1,2,3 >
2025 Major in Mathematics (Intensive) < PLO 1,2,3 >
2024 Major in Mathematics < PLO 1,2,3 >
2024 Major in Mathematics (Intensive) < PLO 1,2,3 >
2023 Major in Mathematics < PLO 1,2,3 >
2023 Major in Mathematics (Intensive) < PLO 1,2,3 >
2022 Major in Mathematics < PLO 1,2,3 >
2022 Major in Mathematics (Intensive) < PLO 1,2,3 >
2021 Major in Mathematics < PLO 1,2,3 >
2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026 Y        2nd sem    Examination May     
Offer in 2026 - 2027 Y
Course Grade A+ to F
Grade Descriptors
A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems.
B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors.
C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors.
D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors.
Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
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 assessment 10.0 1,2,3
Examination 50.0 1,2,3
Test Two midterm tests 40.0 1,2,3
Required/recommended reading
and online materials		 S.M. Ross: Introduction to Probability Models (Academic Press, 2007, 9th ed.)
Course Website http://moodle.hku.hk/
Additional Course Information


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