A first course in mathematical statistics with emphasis on applications; probability, random variables, moment generating functions and correlation, sampling distributions, estimation of parameters by the methods of moments and maximum likelihood, hypothesis testing, the central limit theorem, and Bayesian statistics.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Calculate probabilities using set theory and combinatorics;
2. Use and describe discrete, continuous and multivariate random variables and their probability distributions in simple and complex cases;
3. Define sampling distributions and use the central limit theorem;
4. Explain in detail and use the method of moments and maximum likelihood estimation;
5. Perform confidence estimation and hypothesis testing in a variety of contexts; and
6. Use and describe in detail the fundamental concepts of Bayesian statistics and Bayesian estimators.

Research-Led Teaching

This course, covering classical material in probability and mathematical statistics, is presented through a modern lens and illuminated by recent research where appropriate.

Additional Course Costs

Students will need a non-programmable scientific calculator.

Examination Material or equipment

Only a non-programmable calculator is allowed.

Required Resources

All required course materials will be made available on the course page.

Recommended Resources

Purchase of textbooks is not required for this course. The chapters of the course selectively follow the following textbook available in the ANU Library:

• Wackerly, D.D., Mendenhall III, W., and Scheaffer, R.L. (2008). Mathematical Statistics with Applications, Seventh Edition. Duxbury, Thomson, Brooks/Cole.
• Owen, W.J. (2008). Student Solutions Manual for Wackerly, Mendenhall, and Scheaffer’s Mathematical Statistics with Applications, Seventh Edition. Duxbury, Thomson, Brooks/Cole.

Staff Feedback

Students will be given feedback in the following forms in this course:

• written feedback to two assignments and the in-class test

• verbal feedback from tutors during tutorials and consultation hours

• verbal feedback from the lecturer to the whole class during lectures and individually during consultation hours

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Chapter 1: What Is Statistics? AND Chapter 2: Probability
2	Chapter 2: Probability
3	Chapter 2: Probability
4	Chapter 3: Discrete Random Variables and Their Probability Distributions	Assignment 1 due
5	Chapter 4: Continuous Random Variables and Their Probability Distributions
6	Chapter 5: Multivariate Probability Distributions
7	Chapter 6: Functions of Random Variables	In-class Test
8	Chapter 7: Sampling Distributions and the Central Limit Theorem
9	Chapter 8: Estimation
10	Chapter 9: Properties of Point Estimators and Methods of Estimation
11	Chapter 16: Bayesian Inference	Assignment 2 due
12	Chapter 10: Hypothesis Testing

Tutorial Registration

Tutorials will be available on campus. Tutorial registration will be available via ANU Timetabling two weeks prior to the beginning of the semester and will close on Friday of Week 3. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage (https://www.anu.edu.au/students/program-administration/timetabling)".

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	10 %	14/08/2024	28/08/2024	1
In-class Test	15 %	20/09/2024	04/10/2024	1, 2
Assignment 2	10 %	16/10/2024	30/10/2024	1, 2, 3, 4
Final Exam	65 %	31/10/2024	28/11/2024	1, 2, 3, 4, 5, 6

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines , which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

Course content delivery will take the form of weekly in-person lectures and weekly in-person tutorials on campus. Attendance at lectures and tutorials, while not compulsory, is expected in line with paragraph 2(b) of the ANU Code of Practice for Teaching and Learning. There will be weekly drop-in sessions with the lecturer and tutors for student consultation.

Examination(s)

Centrally scheduled examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.

Assessment Task 1

Assignment 1

This assignment is to be done individually. The assignment, which will contain a mix of theoretical and computational questions, will be released two weeks before the due date and will cover the material from Weeks 1 to 3. Assignment scripts must be submitted via Wattle by midday on the due date and will be returned on the Return of Assessment Date. Any assignment submitted late without an extension approved prior to the assignment deadline will receive a mark of zero.

Assessment Task 2

In-class Test

The in-class test will be 45 minutes long and will take place during lectures (NOT tutorials) in Week 7. It will cover the material from Weeks 1 to 6 and will be invigilated, in person, during the lecture. No materials are allowed other than a non-programmable calculator. It will be redeemable against the final examination.

Assessment Task 3

Assignment 2

This assignment is to be done individually. The assignment, which will contain a mix of theoretical and computational questions, will be released two weeks before the due date and will cover the material from Weeks 1 to 10. Assignment scripts must be submitted via Wattle by midday on the due date and will be returned on the Return of Assessment Date. Any assignment submitted late without an extension approved prior to the assignment deadline will receive a mark of zero.

Assessment Task 4

Final Exam

The final examination is worth 65% of the final raw score and will be centrally invigilated and held on campus in person. Examination materials and conditions will be notified to all students via Wattle no later than Week 10 of the semester. The exam will be centrally timetabled, and details of the final examination timetable will be made available on the ANU Timetabling website.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

Assessment pieces are to be submitted online via Wattle. Please keep a copy of tasks completed for your records.

Hardcopy Submission

Assignments are to be submitted online via Wattle. If you are unable to submit an assignment online, you must bring this to the attention of the course convenor well in advance of the assignment due date.

Late Submission

No submission of assignments after the due date will be permitted without an extension approved by the Convenor before the assignment deadline. If an assignment is not submitted by the due date, and no extension has been approved, a mark of zero will be awarded.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material. Any use of artificial intelligence must be properly referenced. Failure to properly cite use of Generative AI will be considered a breach of academic integrity.

Returning Assignments

Assignments will be returned via Wattle. Students are encouraged to use the consultation time of the tutor and lecturer to obtain further feedback if necessary.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

It will not be possible for assignments to be resubmitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Accessibility for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students