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 ?	BSTA5001
Corequisites ?	None
Prohibitions ?	BSTA5100
Assumed knowledge ?	None
Available to study abroad and exchange students	No

Teaching staff

Coordinator	Erin Cvejic, erin.cvejic@sydney.edu.au

Type	Description	Weight	Due	Length
Assignment	Assignment 1 Written assessment	40%	Week 07	8-10 pages
Outcomes assessed:
Assignment	Assignment 2 Written assessment	60%	Week 13	12-15 pages
Outcomes assessed:

Assessment summary

Assignment 1 will require students to complete numerical and short response questions covering Topics 1 to 6
Assignment 2 will require students to complete numerical and short respond questions covering all Topics (1 to 12)

Additional assessment information will be provided on eLearning

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.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

The standard BCA policy for late penalties for submitted work is a 5% deduction from the earned mark for each day the assessment is late, up to a maximum of 10 days (including weekends and public holidays).

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	Experiments, sample spaces, Probability Rules, Permutations and Combinations	Independent study (10 hr)
Week 02	Conditional Probability, Independence, Bayes’ Theorem	Independent study (10 hr)
Week 03	Random Variables, Probability Functions, Discrete Probability Distributions, Cumulative Distribution functions, Expected value and Variance, Moments	Independent study (10 hr)
Week 04	Important Discrete Distributions: Bernoulli, Binomial, Geometric, and Poisson.	Independent study (10 hr)
Week 05	Moment generating functions. Discrete Distributions: Negative Binomial and Hypergeometric.	Independent study (10 hr)
Week 06	Introduction to Continuous random variables. Cumulative distribution function	Independent study (10 hr)
Week 07	Continuous Distributions: Uniform, Exponential.	Independent study (10 hr)
Week 08	Normal distribution	Independent study (10 hr)
Week 09	Continuous Distributions: Gamma and Beta Distributions. Chebyshev’s Theorem	Independent study (10 hr)
Week 10	Sampling distributions	Independent study (10 hr)
Week 11	Joint Distributions: Discrete and Continuous cases	Independent study (10 hr)
Week 12	Introduction to stochastic processes. Markov Chains.	Independent study (10 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. Analyse probability and conditional probability of an event by applying a probabilistic model for an experiment
LO2. Apply a range of strategies to find and interpret the moments of discrete and continuous random variables including their expected values and variances
LO3. Apply the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) to find asymptotic distribution of a sample mean
LO4. Analyse a bivariate probability distribution to find and interpret corresponding covariances, correlations, marginal and conditional probability distributions
LO5. Apply Markov Chain (MC) theory to practical problems and tasks

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.

PDT was last delivered by Monash University in Semester 2 2021. The current offering was developed by Georgy Sofronov and Houying Zhu from Macquarie University, and is the first time this version of the unit is being delivered into the BCA.

Additional information

This unit is externally delivered through the Biostatistics Collaboration of Australia (BCA).

This is a “legacy” unit made available via teach-out arrangement and delivered by Macquarie University only for students who are tranisitioning between the old (pre-2022) and new (2022) BCA program structures who have completed BSTA5001 (and therefore are not eligible for BSTA5100).

This unit will be delivered via the Macqurie University eLearning platform (iLearn) and timetable.

Biostatistics Collaboration of Australia (BCA)

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

Additional information

Additional information

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

BSTA5023: Probability and Distribution Theory

Semester 1, 2022 [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

Additional information

Additional information

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect