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 elaborates as well as builds upon the statistical principles to which you have been exposed in introductory statistics course/s. The contents and activities in this course are designed to help you to build a mathematical foundation towards a better understanding of statistical theory and methods . Course contents and activities may involve some statistical computing with R interfaced through R Studio, although R codes will not be assessed. Additionally, the group presentation assessment task will involve active collaborations with peers, as well as research and investigation into a mini-topic that extrapolates beyond the course content.

Additional Course Costs

Optional purchase of a non-programmable calculator.

Examination Material or equipment

The final exam will be a take-home exam. As an open book exam, any resource is permitted e.g., you will be able to go online and use probability tables or use statistical software R as appropriate. However collaboration and collusion is not permitted.

Final details of the take home exam, along with all other assessments, will be made available on the Wattle page no later than the end of the intensive week i.e., by 5pm on 12 February.

Recommended Resources

Recommend textbooks and suggested reading (Note these are not compulsory for the course):

• Wackerly, D.D., Mendenhall III, W., and Scheaffer, R.L. (2008). Mathematical Statistics with Applications , Seventh edition.
• Owen, W.J. (2008). Student Solutions Manual for Wackerly, Mendenhall, and Scheaffer’s Mathematical Statistics with Applications, Seventh Edition.
• Ramachandran K.M., and Tsoko C.P. (2015) Mathematical Statistics with Applications in R , Second Edition.
• Devore, J.L. (1991) Probability and Statistics for Engineering and the Sciences.

All of the above texts are available from the ANU library.

Staff Feedback

Feedback from the teaching staff will aim to facilitate the learner's ongoing self assessment of their progress in achieving the learning objectives of the course. To this end, the learner should converse with the teaching staff through Wattle’s discussion forum (preferably) throughout the course, and in-person during the intensive week.

Limited written and verbal comments will also be provided through the grading of assessments tasks. Note that in order to safeguard student privacy, staff members need to be sure that they are dealing with the right student, therefore course-related messages sent from non-ANU email accounts will generally be ignored.

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). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

Information listed in this course summary is tentative, and students will be made aware of any alterations to aspects of the course e.g., changes in assessment due dates, information regarding the structure of the intensive week, via the course Wattle site.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Pre-intensive period (4 weeks remote; Jan 11- Feb 5; each consists of 3 x 1 hour of pre-recorded lectures, and 1 x 2 hour pre-recorded tutorial): C1: Introduction (W1) C2: Probability and probability rules (W1) C3: Discrete random variables (W2) C4: Continuous random variables (W3) C5: Multivariate random variables and probability distributions (W4)	Assignment 1 open and due Group oral presentation open
2	Intensive period (1 week in live online format; Feb 8 - Feb 12; each day consists of 1 x 3.5 hours live lectures + 1 x 2 hours live tutorials. Both tutorials and lectures will be recorded): C6: Functions of random variables C7: Sampling distributions and the central limit theorem C8: Point and interval estimation C9: Hypothesis testing and statistical conference
3	Post-intensive period (4 weeks remote; Feb 15 - Mar 12; there are no classes during this period.)	Assignment 2 open and due Group oral presentation due Take home exam open and due

Tutorial Registration

Tutorial registration is not required.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	20 %	05/02/2021	19/02/2021	1,2
Assignment 2	20 %	26/02/2021	12/03/2021	2,4
Recorded group presentation	15 %	03/03/2021	19/04/2021	1,2,3,4,5,6
Final exam	45 %	11/03/2021	19/04/2021	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 Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

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 ANU Online 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

During the four week pre-intensive period, there will be 3 x 1 hour of pre-recorded lectures, plus 1 x 2 hour of pre-recorded tutorials per week.

During the one-week intensive period, the course will operate in live online (recorded) format. Each day of the intensive week will consists of 1 x 3.5 hour live lectures, plus 1 x 2 hour live tutorial. All lectures and tutorials will be streamed live via Zoom, as well as recorded.

There will be no classes during the post-intensive period.

All assessment tasks will be conducted remotely.

Examination(s)

The course involves one take-home exam, which is tentatively scheduled to take place in the last week of the course (i.e., late post-intensive week 4). You will be required to sign a declaration, in the form of a cover sheet, as part of the submission of your solutions to the take-home exam.

When completing any assessment of the course, students must act in accordance with the University’s Academic Misconduct Rule. Any student identified, either during the current semester or in retrospect, as having used ghost writing services, among other activities that constitute poor academic practice and/or academic misconduct, will be investigated under the University’s Academic Misconduct Rule.

More information about the take home exam, including declaration of acting in accordance with the University’s Academic Misconduct and Poor Academic Practice rules, will be made available no later than the end of the intensive week i.e., by 5pm on 12 February.

Assessment Task 1

Assignment 1

The assignment will be released two weeks before the due date, and assess Chapters/Sections 1-3 of the course. The assignment will consist of six questions, each with multiple parts, and will be similar in level to the tutorial questions.

Due date: Friday 5th February (i.e., end of pre-intensive week 4) @ 5:00 pm Canberra Time

Value: 20%

Assessment Task 2

Assignment 2

The assignment will be released two weeks before the due date, and assess Chapters/Sections 4-6 of the course. The assignment will consist of six questions, each with multiple parts, and will be similar in level to the tutorial questions.

Due date: Friday 26th February (i.e., end of post-intensive week 2) @ 5:00 pm Canberra Time

Value: 20%

Assessment Task 3

Recorded group presentation

Topics for the group presentation will be made available on Friday 5th February (i.e., end of pre-intensive week 4). The group presentation will build upon all nine chapters/sections of the course, and require the students to research investigate a topic that extends them beyond the course content (in line with research-led and research-oriented teaching, and formative assessment), and then record a short presentation of up to ten mins discussing their findings and results. There is no written report associated with this assessment task.

Each group will have a maximum of three students.

As this is a group assessment, please ensure you adhere to the required social distancing requirements, e.g. using Zoom for meetings. Note live, in-person presentations will not be taking place. Instead, students are to record their presentations and submit them online e.g., a video file or a hyperlink to the video.

Due date: Wednesday March 3rd (i.e., middle of post-intensive week 3) @ 5pm Canberra Time

Value: 15%

Assessment Task 4

Final exam

Details of the final take-home will be announced on Wattle no later than the end of the intensive week. The exam will assess all nine chapters/sections of the course, as well as build on the Assessment Task 3. The exam will consist of four questions, each with multiple parts, and will be at a level similar to that of the Assessment Tasks 1-2, and with the tutorial questions.

Due date: The take-home exam is tentatively scheduled to take place on Thursday March 11(i.e., late post-intensive week 4).

Value: 45%

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to sign a declaration, in the form of a cover sheet, as part of the submission of your assignment. Please keep a copy of the assignment and signed cover sheets, for your record.

Each assignment and the final take-home exam must be submitted as a single electronic file, preferably a pdf, to the appropriate activity on the course Wattle site. If submitting handwritten mathematical derivations, ensure that your handwriting is legible, appropriate working out is shown, and then scan the derivations in e.g., by using your smartphone camera. The group presentation is a recorded video file, and will either be submitted as a video file or a hyperlink to the video,to the appropriate activity on the course Wattle site.

More information about online submissions of each assessments task will be given on the course Wattle site.

Hardcopy Submission

Hardcopy submissions will not be used in this course.

Late Submission

No submission of any assessment tasks without an approved extension after the due date is permitted. If an assessment task is not submitted by the due date, then unless an extension has been approved, a mark of zero will be awarded.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Graded assignments along with feedback should be made available via the relevant activity on the course Wattle site approximately 14 days after the due date.

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

Resubmission of assessments is not allowed under any circumstance.

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 Diversity and inclusion 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 and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students