Outline

Overview

This unit offers a foundational introduction to probability theory and statistical inference, focusing on key concepts such as random variables and widely used probability distributions—including the Binomial, Hypergeometric, Poisson, Normal, Geometric, and Gamma distributions. Students will engage with univariate data analysis techniques and gain practical skills in modelling variability using real-world data. Core estimation methods, including the method of moments, maximum likelihood estimation, and associated inference procedures are introduced in a rigorous yet accessible manner. Weekly computer laboratory sessions provide hands-on experience with statistical software for simulation, distribution fitting, and computational methods such as the bootstrap. By the end of the unit, students will have developed essential statistical modelling competencies, equipping them for further study in advanced statistical analysis and data science.

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 (DATA1X01 or MATH1X62 or MATH1972 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020)
Corequisites ?	None
Prohibitions ?	STAT2911
Assumed knowledge ?	None
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Shelton Peiris, shelton.peiris@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 Short answer questions and extended answer questions	60%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Data analysis	Computer Class Reports Online submission of 3 computer lab reports in weeks 4, 8 and 12.	6%	Multiple weeks	Variable	AI allowed
Outcomes assessed:
Contribution	Weekly tutorial and workshop attendence Individual participation of 10 tutorials and 10 workshops in Semester 1, 2026. Each class is worth 0.2 marks.	4%	Multiple weeks	2 hours (1 hr tutorials;1 hr workshops)	AI allowed
Outcomes assessed:
Out-of-class quiz	Early Feedback Task Online Task, see Canvas for details	5%	Week 03 Due date: 13 Mar 2026 at 23:00 Closing date: 13 Mar 2026	40 mins	AI allowed
Outcomes assessed:
In-class quiz	Quiz 1 In-class quiz 1, during last lecture of Week 5	10%	Week 05 Due date: 25 Mar 2026 at 11:00 Closing date: 25 Mar 2026	40 mins	AI allowed
Outcomes assessed:
In-class quiz	Quiz 2 In-class quiz 2, during last lecture of Week 11	10%	Week 11 Due date: 13 May 2026 at 11:00 Closing date: 13 May 2026	40 mins	AI allowed
Outcomes assessed:
Data analysis	Assignment Assignment	5%	Week 12 Due date: 22 May 2026 at 23:00 Closing date: 22 May 2026	3-6 pages/1 week	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

Detailed information for each assessment can be found on Canvas.

Final exam: If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.
Two in person supervised quizzes will be held in lectures times weeks 5 (25/03/2026) and 11 (13/05/2026) from 10.00 to11.00 am. No replacement quizzes will be given. If you miss a quiz, please apply for special consideration with acceptable reasons. If it is accepted, mark adjustment will be carried out.
Tutorial and Workshop Contributions: This is a satisfactory/non-satisfactory mark assessing whether or not you contribute to class activities during the tutorials and workshops starting in Week 2. It is 0.2 marks per tutorial or workshop up to 10 tutorials and 10 workshops (there are 12 tutorials and 12 workshops).

Assessment criteria

Result name	Mark range	Description
High distinction	85 - 100	At HD level, a student demonstrates a flair for the subject as well as a detailed and comprehensive understanding of the unit material. A ‘High Distinction’ reflects exceptional achievement and is awarded to a student who demonstrates the ability to apply their subject knowledge and understanding to produce original solutions for novel or highly complex problems and/or comprehensive critical discussions of theoretical concepts.
Distinction	75 - 84	At DI level, a student demonstrates an aptitude for the subject and a well-developed understanding of the unit material. A ‘Distinction’ reflects excellent achievement and is awarded to a student who demonstrates an ability to apply their subject knowledge and understanding of the subject to produce good solutions for challenging problems and/or a reasonably well-developed critical analysis of theoretical concepts.
Credit	65 - 74	At CR level, a student demonstrates a good command and knowledge of the unit material. A ‘Credit’ reflects solid achievement and is awarded to a student who has a broad general understanding of the unit material and can solve routine problems and/or identify and superficially discuss theoretical concepts.
Pass	50 - 64	At PS level, a student demonstrates proficiency in the unit material. A ‘Pass’ reflects satisfactory achievement and is awarded to a student who has threshold knowledge.
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
Week 01	1. Introduction; 2. Sample spaces and the algebra sets; 3. The probability function; 4. Conditional probability	Lecture (3 hr)
Week 02	1. Independence; 2. Combinatorics	Lecture (3 hr)
	1. Independence; 2. Combinatorics	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 03	1. Combinatorial probability; 2. Discrete random variables; 3. Expected value and variance	Lecture (3 hr)
	1. Combinatorial probability; 2. Discrete random variables; 3. Expected value and variance	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 04	1. Binomial random variables 2. Poisson random variables 2. Hypergeometric random variables	Lecture (3 hr)
	1. Binomial random variables 2. Poisson random variables 2. Hypergeometric random variables	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 05	1. Other discrete random variables 2. Continuous random variables 3. Expected value and variance 4. Uniform random variables	Lecture (3 hr)
	1. Other discrete random variables 2. Continuous random variables 3. Expected value and variance 4. Uniform random variables	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 06	1. Normal random variables 2. Gamma random variables	Lecture (3 hr)
	1. Normal random variables 2. Gamma random variables	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 07	1. Joint densities; 2. Transforming and combining random variables;	Lecture (3 hr)
	1. Joint densities; 2. Transforming and combining random variables;	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 08	1. Order statistics 2. Conditional densities 3. Moment generating function	Lecture (3 hr)
	1. Order statistics 2. Conditional densities 3. Moment generating function	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 09	1. Estimation theory	Lecture (3 hr)
	1. Estimation theory	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 10	1. Estimating parameters	Lecture (3 hr)
	1. Estimating parameters	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 11	1. Interval estimation	Lecture (3 hr)
	1. Interval estimation	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 12	1. Properties of estimation	Lecture (3 hr)
	1. Properties of estimation	Tutorial (1 hr)
	Computer lab	Workshop (1 hr)
Week 13	Revision	Lecture (3 hr)
	Revision	Tutorial (1 hr)
	Computer lab	Workshop (1 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.

Required readings

The formal textbooks for the course are

Larsen, R. J., & Marx, M. L. (2005). An introduction to mathematical statistics. Prentice Hall.

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.

No changes have been made since this unit was last offered

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

Required readings

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

STAT2011: Probability and Estimation Theory

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

Required readings

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