SDST3902 Mathematical statistics (6 credits) 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 a rigorous introduction to fundamental concepts in probability and mathematical statistics, including stochastic modelling, independence and dependence, summary statistics, conditional expectation and distributions, asymptotic theory, point and interval estimation and hypothesis testing. It is an approved Validation by Educational Experience (VEE) course by the Society of Actuaries (SOA).
Course Contents & Topics Probability spaces, random variables and random vectors, univariate and multivariate distribution functions, empirical distribution functions, quantile functions, independence and dependence, covariance, correlation, multivariate notions, conditional expectation and distributions, modes of convergence, continuous mapping theorem and Slutsky's theorem, strong law of large numbers, central limit theorem, estimation concepts, constructing uniformly minimum variance unbiased estimators, exact and asymptotic confidence intervals, nonparametric bootstrap, method of moments estimator, maximum likelihood estimator and asymptotic properties, hypothesis testing concepts, size and power, p-values, (uniformly) most powerful tests, likelihood ratio test.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 understand the fundamentals of probability in the univariate and multivariate case
CLO 2 understand the fundamentals of probabilistic modelling
CLO 3 learn about concepts in mathematical statistics
CLO 4 understand the concepts of point estimation, interval estimation and hypothesis testing
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in SDST2901; and
Not for students who have passed in SDST2602, or already enrolled in this course; and
For BSc(Actuarial Science) students only.
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
2024 BSc in Actuarial Science ( Core/Compulsory )
2023 BSc in Actuarial Science ( Core/Compulsory )
2022 BSc in Actuarial Science ( Core/Compulsory )
2021 BSc in Actuarial Science ( Core/Compulsory )
Course to PLO Mapping 2024 BSc in Actuarial Science < PLO 1,3,5 >
2023 BSc in Actuarial Science < PLO 1,3,5 >
2022 BSc in Actuarial Science < PLO 1,3,5 >
2021 BSc in Actuarial Science < PLO 1,3,5 >
Offer in 2025 - 2026 Y        1st sem    Examination Dec     
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		 Casella G., Berger R. L.:  Statistical Inference, 2nd edition, Duxbury, 2001.
Course Website http://moodle.hku.hk
Additional Course Information NIL