A first course in mathematical statistics for actuarial studies 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, Bayesian statistics and credibility theory. 

Learning Outcomes

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

1. Calculate probabilities using set theory and combinatorics;
2. Define and utilise discrete, continuous and multivariate random variables and their probability distributions;
3. Define sampling distributions and use the central limit theorem in a variety of contexts;
4. Explain in detail and perform 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, including credibility estimators.

Research-Led Teaching

If time permits, the lecturers may illustrate selected topics by discussing relevant examples from papers they have published. New material in these examples will not be assessable.

Additional Course Costs

Students will need a non-programmable scientific calculator.

Examination Material or equipment

You will require reliable assess to Wattle and a calculator for the duration of the online quizzes and the online exam.

Recommended Resources

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.

The ANU Library has been requested to order the e-book.

Staff Feedback

Students will be given feedback (through both verbal and written comments) in the following forms in this course:

• To the whole class during lectures.

• Within tutorials.

• Individually during consultation hours.

Students will also be given online quiz feedback on Wattle and written comments in the marked assignments.

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

Support for Students

The University offers a number of support services for students. Information on these is available online from http://students.anu.edu.au/studentlife/

Communication via Email

If I, or anyone in the School, College or University administration, need to contact you, we will do so via your official ANU student email address, which you need to check regularly. If you have any questions for the teaching and course convenor make sure you email them using your ANU email address. Emails from personal email accounts will not be answered.

Announcements

Students are expected to check the Wattle site for announcements about this course, e.g. changes to timetables or notifications of cancellations.

Assessment Requirements

Any student identified, either during the current semester or in retrospect, as having used ghost writing services will be investigated under the University’s Academic Misconduct Rule.

Scaling

Your final mark for the course will be based on the raw marks allocated for each of your assessment items. However, your final mark may not be the same number as produced by that formula, as marks may be scaled. Any scaling applied will preserve the rank order of raw marks (i.e. if your raw mark exceeds that of another student, then your scaled mark will exceed the scaled mark of that student), and may be either up or down.

Referencing Requirements

In assignments and exams, students must appropriately reference any results, words or ideas that they take from another source which is not their own. A guide can be found at https://academicskills.anu.edu.au/resources/handouts/referencing-basics.

Co-Teaching

STAT6013 shares the same lecture content and assignments with STAT2001, STAT2013 and STAT6039 cohorts, however these cohorts may have separate tutorials and different assessments. Students in STAT6013 also have some additional lecture content that STAT6039 students are not required to take. The different cohorts of students will also be treated separately in grading and any scaling that is applied.

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
5	Chapter 4: Continuous Random Variables and Their Probability Distributions
6	Chapter 5: Multivariate Probability Distributions	Wattle Quiz
7	Chapter 6: Functions of Random Variables	Release of Assignment 1 via Wattle
8	Chapter 7: Sampling Distributions and the Central Limit Theorem
9	Chapter 8: Estimation	Submission of Assignment 1 via Wattle; Release of Assignment 2 via Wattle
10	Chapter 9: Bayesian Inference AND Chapter 11: Credibility Theory (extra lecture)
11	Chapter 10: Hypothesis Testing AND Chapter 11: Credibility Theory (extra lecture)	Submission of Assignment 2 via Wattle
12	Chapter 10: Hypothesis Testing AND Chapter 11: Credibility Theory (extra lecture); Course Review	There will be a final exam during the university examination period. More information and instructions regarding the exam will be provided no later than week 10 on Wattle.

Tutorial Registration

Tutorials will be available on campus, live through scheduled Zoom sessions and as pre-recorded videos. Information regarding enrolments for these options will be provided on Wattle during O-week of the semester.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Quiz	5 %	03/09/2021	03/09/2021	1,2
Assignment 1	15 %	06/10/2021	15/10/2021	1,2
Assignment 2	15 %	22/10/2021	29/10/2021	1,2,3,4
Final Exam	65 %	04/11/2021	02/12/2021	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 Academic Integrity . 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 pre-recorded weekly lectures (available via echo360 on Wattle), and weekly tutorials, delivered in hybrid format (on campus, live through scheduled Zoom sessions and as pre-recorded videos).

Examination(s)

Any student identified, either during the current semester or in retrospect, as having used ghost writing services will be investigated under the University’s Academic Misconduct Rule. 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

Quiz

This quiz is worth 5% of the final raw score and is redeemable. An assessment is redeemable if, when a student performs better in the final exam than in the assessment, then the final exam mark will count instead of the assessment. The students are expected to complete this quiz individually. The quiz will be designed to cover materials from Week 1 to Week 5 and will be open for 3 days in Week 6. Once commenced, students will have 1 hour to complete and submit the quiz. The notification about access to the quiz will be announced in Week 5 during lectures and on Wattle. Under no circumstances will the students be able to attempt the quiz outside of the allocated time period. There will be a mix of multiple-choice and numerical calculation questions.

Assessment Task 2

Assignment 1

The students are expected to complete this assignment individually. This assignment is designed to cover materials from Week 1 to 7. It is worth 15% of the final raw score and is redeemable. The assignment and further details will be made available on Wednesday in Week 7. It will be due on Wednesday in Week 9. There will be a mix of numerical calculation questions and theoretical proofs.

Assessment Task 3

Assignment 2

The students are expected to complete this assignment individually. This assignment is designed to cover materials from Week 1 to 9. It is worth 15% of the final raw score and is redeemable. The assignment and further details will be made available on Friday in Week 9. It will be due on Friday in Week 11. There will be a mix of numerical calculation questions and theoretical proofs.

Assessment Task 4

Final Exam

The final examination will be a Wattle-based online exam during the university examination period at the end of the semester. The final examination will be around 3 hours long and cover the entire syllabus. It will be open book and all materials are permitted. The final examination is worth 65% of the final raw score. There will be a mix of numerical calculation questions and theoretical proofs in the exam. 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. 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 electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

There is no hardcopy submission in the course.

Late Submission

No submission of assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 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

The marked assignments will be returned online.

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 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