Skip to main content
Unit of study_

STAT2011: Probability and Estimation Theory

Semester 1, 2022 [Normal day] - Remote

This unit provides an introduction to probability, the concept of random variables, special distributions including the Binomial, Hypergeometric, Poisson, Normal, Geometric and Gamma and to statistical estimation. This unit will investigate univariate techniques in data analysis and for the most common statistical distributions that are used to model patterns of variability. You will learn the method of moments and maximum likelihood techniques for fitting statistical distributions to data. The unit will have 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. By doing this unit you will develop your statistical modelling skills and it will prepare you to learn more complicated statistical models.

Unit details and rules

Unit code STAT2011
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
(MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020)
Assumed knowledge


Available to study abroad and exchange students


Teaching staff

Coordinator Clara Grazian,
Lecturer(s) Clara Grazian,
Type Description Weight Due Length
Final exam (Record+) Type B final exam Final exam
Short answer questions and extended answer questions
60% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6
Assignment Computer class reports
Online submission of 3 computer lab reports
5% Multiple weeks Variable
Outcomes assessed: LO1 LO2 LO3 LO4
Tutorial quiz Quiz 1
Online quiz 1 on 23/03/2022, 12.00-13.00
10% Week 05
Due date: 23 Mar 2022 at 13:00
45 mins
Outcomes assessed: LO1 LO6 LO5 LO2
Tutorial quiz Quiz 2
Online quiz 2 on 11/05/2022, 12.00-13.00
10% Week 11
Due date: 11 May 2022 at 13:00
45 mins
Outcomes assessed: LO1 LO6 LO5 LO4 LO3 LO2
Assignment Assignment
15% Week 12
Due date: 27 May 2022 at 23:59
48 hrs
Outcomes assessed: LO1 LO4 LO3 LO2
Type B final exam = Type B final exam ?

Assessment summary

Detailed information for each assessment can be found on Canvas.

  • Better mark principle: The better mark principle means that the STAT2011 quiz marks count if and only if they are better than or equal to the exam mark. If either mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead. The computer reports and test count regardless of whether they are better than your exam mark or not.
  • 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. 

Assessment criteria

Result name

Mark range


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.


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.


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.


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.


0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

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 Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.  

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

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.

WK Topic Learning activity Learning outcomes
Week 01 1. Introduction; 2. Sample spaces and the algebra sets; 3. The probability function; 4. Conditional probability Lecture and tutorial (5 hr)  
Week 02 1. Independence; 2. Combinatorics Lecture and tutorial (5 hr)  
Week 03 1. Combinatorial probability; 2. Taking a second look at the statistics; 3. Introduction; 4. Binomial probability function; 5. The hypergeometric distribution; 6. Discrete random variables Lecture and tutorial (5 hr)  
Week 04 1. Continuous random variables; 2. Expected values Lecture and tutorial (5 hr)  
Week 05 1. Variance; 2. Joint densities Lecture and tutorial (5 hr)  
Week 06 1. Joint densities; 2. Transforming and combining random variables; 3. Further properties of the mean and variance Lecture and tutorial (5 hr)  
Week 07 1. Order statistics; 2. Conditional densities Lecture and tutorial (5 hr)  
Week 08 1. Moment-generating functions; 2. The Poisson distribution; 3. The Normal distribution Lecture and tutorial (5 hr)  
Week 09 1. The Normal distribution; 2. The Geometric distribution; 3. The negative binomial distribution Lecture and tutorial (5 hr)  
Week 10 1. The Gamma distribution; 2. Estimating parameters Lecture and tutorial (5 hr)  
Week 11 1. Estimating parameters; 2. Interval estimation Lecture and tutorial (5 hr)  
Week 12 1. Interval estimation; 2. Properties of estimation Lecture and tutorial (5 hr)  
Week 13 Revision Lecture and tutorial (5 hr)  
Weekly Computer lab Computer laboratory (1 hr) LO1 LO2 LO3 LO4 LO5 LO6

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 textbook for the course is An Introduction to Mathematical Statistics and Its Applications (any edition) by Richard J. Larsen and Morris L. Marx.

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.

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

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

No changes have been made since this unit was last offered

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:


The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

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