Outline

Overview

This unit will focus on applying the calculus-based techniques learned in Mathematical Background for Biostatistics (MBB) to the study of probability and statistical distributions. These two units, together with the subsequent Principles of Statistical Inference (PSI) unit, will provide the core prerequisite mathematical statistics background required for the study of later units in the Graduate Diploma or Masters degree. Content: This unit begins with the study of probability, random variables, discrete and continuous distributions, and the use of calculus to obtain expressions for parameters of these distributions such as the mean and variance. Joint distributions for multiple random variables are introduced together with the important concepts of independence, correlation and covariance, marginal and conditional distributions. Techniques for determining distributions of transformations of random variables are discussed. The concept of the sampling distribution and standard error of an estimator of a parameter is presented, together with key properties of estimators. Large sample results concerning the properties of estimators are presented with emphasis on the central role of the Normal distribution in these results. General approaches to obtaining estimators of parameters are introduced. Numerical simulation and graphing with Stata is used throughout to demonstrate concepts.

Unit details and rules

Academic unit	Public Health
Credit points	6
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	None
Assumed knowledge ?	None
Available to study abroad and exchange students	No

Teaching staff

Coordinator	Patrick Kelly (Public Health), p.kelly@sydney.edu.au

Type	Description	Weight	Due	Length
Assignment	Assignment 2 This assessment covers modules 1 to 6.	35%	STUVAC	10 pages
Outcomes assessed:
Assignment	Module 1 exercises Covers Module 1 material	5%	Week 03	3 pages
Outcomes assessed:
Assignment	Module 2 exercises Covers Module 2 material.	5%	Week 04	3 pages
Outcomes assessed:
Assignment	Module 3 exercises Covers Module 3 material.	10%	Week 07	3 pages
Outcomes assessed:
Assignment	Assignment 1 This assessment covers models 1 to 3.	35%	Week 08	10 pages
Outcomes assessed:
Assignment	Module 4 exercises This assessment covers Module 4.	5%	Week 10	3 pages
Outcomes assessed:
Assignment	Module 5 exercises This assessment covers Module 5.	5%	Week 13	3 pages
Outcomes assessed:

Assessment summary

Assessment will include 2 major written assignments worth 35% each, to be made available in the middle and at the end of the semester, and to be completed within approximately 2 weeks. Assignment 1 will cover material from Modules 1-3 only. Assignment 2 will cover the entire semester’s material, but with emphasis on Modules 4 and 5.

In addition, students will be required to submit solutions to selected practical exercises from each module, worth a total of 30%,

Assessment criteria

Grade	Mark Range	Description
AF Absent fail	Range from 0 to 49	To be awarded to students who fail to demonstrate the learning outcomes for the unit at an acceptable standard through failure to submit or attend compulsory assessment tasks or to attend classes to the required level. In cases where a student receives some marks but fails the unit through failure to attend or submit a compulsory task, the mark entered shall be the marks awarded by the faculty up to a maximum of 49. This grade should not be used in cases where a student attempts all assessment tasks but fails to achieve a mandated minimum standard in one or more task. In such cases a Fail (FA) grade and a mark less than 50 should be awarded.
FA Fail	Range from 0 to less than 50	To be awarded to students who, in their performance in assessment tasks, fail to demonstrate the learning outcomes for the unit at an acceptable standard established by the faculty. This grade, with corresponding mark, should also be used in cases where a student fails to achieve a mandated standard in a compulsory assessment, thereby failing to demonstrate the learning outcomes to a satisfactory standard.
PS Pass	Range from 50 to less than 65	To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at an acceptable standard
CR Credit	Range from 65 to less than 75	To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at a good standard
D Distinction	Range from 75 to less than 85	To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at a very high standard
HD High distinction	Range from 85 to 100 inclusive	To be awarded to students who, in their performance in assessment tasks, demonstrate the learning outcomes for the unit at an exceptional 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.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

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.

Weekly schedule

WK	Topic	Learning activity
Week 01	Module 1: Probability	Individual study (20 hr)
Week 03	Module 2: Discrete Random variables	Individual study (20 hr)
Week 05	Module 3: Continuous random variables	Individual study (30 hr)
Week 09	Module 4: Multiple random variables	Individual study (20 hr)
Week 11	Module 5: Estimation	Individual study (30 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. Demonstrate an understanding of the meaning and laws of probability
LO2. Recognise common probability distributions and their properties
LO3. Apply calculus-based tools to derive key features of a probability distribution, such as mean and variance
LO4. Obtain mean, variance and the probability distribution of transformations of random variables
LO5. Manipulate multivariate probability distributions to obtain marginal and conditional distributions
LO6. Understand properties of parameter estimators and the usefulness of large sample approximations in statistics
LO7. Appreciate the role of simulation in demonstrating and explaining statistical concepts

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.

Disclaimer

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.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

BSTA5023: Probability and Distribution Theory

Semester 1, 2021 [Online] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect