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 their research area. New material in these examples will not be assessable.

Additional Course Costs

Students will need a non-programmable scientific calculator.

Examination Material or equipment

Examination material and conditions will be notified to all students via Wattle and the examinations office.

Required Resources

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-books.

Staff Feedback

Consultation times will be finalised at the start of the semester.

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

· Verbal communication from lecturers and tutors, individually upon request.

· Marks and summaries for the assignments and quiz.

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.

Other Information

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, 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

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/

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	Quiz via Wattle
6	Chapter 5: Multivariate Probability Distributions
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: Properties of Point Estimators and Methods of Estimation 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)	There will be a final exam during the university examination period. More information and instructions regarding final exams will be provided no later than the week 10 lectures.

Tutorial Registration

Tutorials will be available on campus, live through scheduled Zoom sessions and as pre-recorded videos. Students should enrol in their tutorial using MyTimetable.

"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)".

 "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)".

 

 

If you need to change your enrolment, you will be able to do so by clicking on the tab “Leave group….” and then re-enrol in another group. You will not be able to enrol in groups that have reached their maximum number. Please note that enrolment in ISIS must be finalised for you to have access to Wattle.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Quiz	5 %	22/08/2022	29/08/2022	1,2
Assignment 1	15 %	19/09/2022	03/10/2022	1,2
Assignment 2	15 %	07/10/2022	21/10/2022	1,2,3,4
Final exam	65 %	03/11/2022	01/12/2022	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
• Special Assessment Consideration Guideline and General Information 
• 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

Attendance and participation in lectures and tutorials is recommended but not assessable. Course content delivery will take the form of on campus weekly lectures, one additional online lecture in each of Weeks 9-12, 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

Students will get about 60-90 minutes to complete this quiz individually via Wattle. This quiz is designed to cover materials from Week 1 to Week 4. This quiz is worth 5% of your final raw score. The quiz will be available on Wattle in Week 5. The notification about access to the quiz will be announced in Week 4 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. Results will be released by the end of Week 6.

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 6. It is worth 15% of the final raw score. The assignment and further details will be made available on Monday in Week 7. It will be due on Monday 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. 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

This final exam will be based on all the materials covered throughout the duration of the semester. The final examination is worth 65% of the final raw score. Students will be provided with further details regarding the exam no later than the week 10. There will be a mix of numerical calculation questions and theoretical proofs. 3 November 2022 is the earliest date the exam can be held. 

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

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

Online submission only.

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

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.

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 Access 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