Outline

Overview

This unit is essentially an advanced version of STAT2011, with an emphasis on the mathematical techniques used to manipulate random variables and probability models. Common distributions including the Poisson, normal, beta and gamma families as well as the bivariate normal are introduced. Moment generating functions and convolution methods are used to understand the behaviour of sums of random variables. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The notions of conditional expectation and prediction will be covered as will be distributions related to the normal: chi^2, t and F. The unit has weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	(MATH1X61 or MATH1971 or MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and a mark of 65 or greater in (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020 or MATH1X62 or MATH1972)
Corequisites ?	None
Prohibitions ?	STAT2011
Assumed knowledge ?	None
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Clara Grazian, clara.grazian@sydney.edu.au

Assessment

The census date for this unit availability is 31 March 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam	Final exam Final exam	60%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Out-of-class quiz	Early Feedback Task Early Feedback Task	4%	Week 03 Due date: 13 Mar 2026 at 17:00 Closing date: 23 Mar 2026	30 minutes	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz 1 Multiple choice and short answer questions	10%	Week 05 Due date: 25 Mar 2026 at 10:00 Closing date: 25 Mar 2026	45 mins	AI prohibited
Outcomes assessed:
Out-of-class quiz	Computer Assignment 1 Short answer questions	8%	Week 06 Due date: 02 Apr 2026 at 17:00 Closing date: 12 Apr 2026	2-4 pages (around 10 questions)	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz 2 Multiple choice and short answer questions	10%	Week 11 Due date: 13 May 2026 at 10:00 Closing date: 13 May 2026	45 mins	AI prohibited
Outcomes assessed:
Out-of-class quiz	Computer Assignment 2 Short answer questions	8%	Week 12 Due date: 22 May 2026 at 17:00 Closing date: 01 Jun 2026	2-4 pages (around 10 questions)	AI allowed
Outcomes assessed:
= early feedback task ?

Early feedback task

This unit includes an early feedback task, designed to give you feedback prior to the census date for this unit. Details are provided in the Canvas site and your result will be recorded in your Marks page. It is important that you actively engage with this task so that the University can support you to be successful in this unit.

Assessment summary

Late submission is only allowed for the assignment while incurring the standard late submisison penalties.

Quizzes will take place while supervised in class and with closed books (formulas needed will provided/allowed). If Special Considerations are approved, a mark adjustment will be awarded.

Final exam will be supervised with closed books but with formulas provided.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name	Mark range	Description
High distinction	85 - 100	Representing complete or close to complete mastery of the material.
Distinction	75 - 84	Representing excellence, but substantially less than complete mastery.
Credit	65 - 74	Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
Pass	50 - 64	Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.
Fail	0 - 49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the Academic Integrity Policy.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the Academic Honesty Education Module (AHEM) which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Multiple weeks	Weeks 1-13: Tutorials covering questions related to content from the previous week	Tutorial (13 hr)
Multiple weeks	Weeks 1-13: Demonstration of practice questions and computer worksheets related to content from current week.	Workshop (13 hr)
Week 01	Probability spaces & counting. Sample spaces and events; Probability measures (light formalism); Counting tools	Lecture (3 hr)
Week 02	Conditional probability & independence. Conditional probability; Bayes’ rule & total probability; Independence	Lecture (3 hr)
Week 03	Random variables & distributions. Random variables; CDFs; PMFs and PDFs	Lecture (3 hr)
Week 04	Core distributions. Discrete distributions; Continuous distributions; Modelling with distributions	Lecture (3 hr)
Week 05	Expectation, variance & inequalities.	Lecture (3 hr)
Week 06	Moments, MGFs & transformations of random variables.	Lecture (3 hr)
Week 07	Samples, Empirical Distributions, and Random Statistics	Lecture (3 hr)
Week 08	Point Estimation and Optimality Concepts	Lecture (3 hr)
Week 09	Likelihood-based inference	Lecture (3 hr)
Week 10	Interval estimation	Lecture (3 hr)
Week 11	Hypothesis testing	Lecture (3 hr)
Week 12	Asymptotic theory	Lecture (3 hr)

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. construct appropriate statistical models involving random variables for a range of modelling scenarios. Compute (or approximate with a computer if necessary) numerical characteristics of random variables in these models such as probabilities, expectations and variances
LO2. fit such models in outcome 1. to data (as appropriate) by estimating any unknown parameters
LO3. compute appropriate (both theoretically and computationally derived) measures of uncertainty for any parameter estimates
LO4. assess the goodness of fit (as appropriate) of a fitted model
LO5. apply certain mathematical results (e.g. inequalities, limiting results) to problems relating to statistical estimation theory
LO6. prove certain mathematical results (e.g. inequalities, limiting results) used in the course.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

Assessment structure and outline has been changed in S1 2026.

Additional information

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

No eating or drinking is allowed in any laboratory under any circumstances
A laboratory coat and closed-toe shoes are mandatory
Follow safety instructions in your manual and posted in laboratories
In case of fire, follow instructions posted outside the laboratory door
First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

Important: the University of Sydney regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

STAT2911: Probability and Statistical Models (Adv)

Semester 1, 2026 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links