SDST2602 Probability and statistics II (6 credits) Academic Year 2025
Offering Department SCDS (Department of Statistics and Actuarial Science) Quota ---
Course Co-ordinator Prof L Feng, SCDS (Department of Statistics and Actuarial Science) < lfeng@hku.hk >
Teachers Involved (Prof L Feng,Statistics & Actuarial Science)
Course Objectives This course builds on SDST2601, introducing further the concepts and methods of statistics. Emphasis is on the two major areas of statistical analysis: estimation and hypothesis testing.  Through the disciplines of statistical modelling, inference and decision making, students will be equipped with both quantitative skills and qualitative perceptions essential for making rigorous statistical analysis of real-life data.
Course Contents & Topics 1. Overview: random sample; sampling distributions of statistics; moment generating function; large-sample theory: laws of large numbers and Central Limit Theorem; likelihood; sufficiency; factorisation criterion;
2. Estimation: estimator; bias; mean squared error; standard error; consistency; Fisher information; Cramer-Rao Lower Bound; efficiency; method of moments; maximum likelihood estimator;
3. Hypothesis testing: types of hypotheses; test statistics; p-value; size; power; likelihood ratio test; Neyman-Pearson Lemma; generalized likelihood ratio test; Pearson chi-squared test; Wald tests;
4. Confidence interval: confidence level; confidence limits; equal-tailed interval; construction based on hypothesis tests.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 apprehend the objectives of statistics and its relation to probability theory
CLO 2 relate a real-life problem to a formal framework for statistical inference
CLO 3 conduct standard parametric statistical inference by means of estimation and hypothesis testing
CLO 4 reckon the general applicability of statistics in a broad range of subject areas
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in SDST2601; and
Not for students who have passed in SDST3902, or already enrolled in this course.
Only for students admitted in 2025 and thereafter.
Course Status with Related Major/Minor/Professional Core 2025 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2025 Bachelor of Engineering in Artificial Intelligence and Data Science ( Core/Compulsory )
2025 Bachelor of Statistics ( Core/Compulsory )
2025 Major in Decision Analytics ( Core/Compulsory )
2025 Major in Risk Management ( Core/Compulsory )
2025 Major in Statistics ( Core/Compulsory )
2025 Minor in Risk Management ( Disciplinary Elective )
2025 Minor in Statistics ( Disciplinary Elective )
Course to PLO Mapping 2025 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 1,2,3 >
2025 Professional Core in Decision Analytics < PLO 1,2,3,4,5 >
2025 Professional Core in Risk Management < PLO 2,3,4 >
2025 Professional Core in Statistics < PLO 1,2,4,5,6 >
Offer in 2025 - 2026 Y        1st sem    2nd sem    Examination Dec    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		 Berry, D.A. & Lindgren, B.W. (1996).  Statistics: Theory and Methods. Duxbury: Belmont.
Bickel, P.J. & Doksum, K.A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics. Prentice Hall: Upper Saddle River, N.J.
Hogg, R.V. & Craig, A.T. (1989). Introduction to Mathematical Statistics. Macmillan: New York.
Miller, I. & Miller, M. (2004). John E. Freund's Mathematical Statistics with Applications. Pearson Prentice Hall: Upper Saddle River.
Course Website http://moodle.hku.hk
Additional Course Information NIL