The unit develops foundation skills for the analysis of real-life systems with elements of uncertainty, useful for careers in the Physical and Biological Sciences, Operations Research, Statistics, Engineering, Computer Science, Finance and Economics. The unit covers major topics from Probability Theory, with the focus on developing in-depth knowledge from both theoretical and modelling points of view.
Topics: Axiomatic probability theory: sample space, event, probabilities on events, independent events, Bayes' formula; Random variable, probability distribution, expectation, conditional probability; Distribution functions: discrete, continuous; joint distribution; probability generating function; Laplace transform; moment generating function; limit theorems. Stochastic Processes: Bernoulli process; Poisson process; discrete-time Markov Chains: Chapman-Kolmogorov equations, classification of states, recurrence, limiting probabilities; continuous-time Markov Chains: Kolmogorov differential equations, embedded chains, equilibrium distributions.
Students will use MATLAB for the numerical experimentation.
|Unit name||Probability Models 3|
|College/School||College of Sciences and Engineering
School of Natural Sciences
|Coordinator||Associate Professor Malgorzata O'Reilly|
|Available as student elective?||Yes|
|Delivered By||Delivered wholly by the provider|
|Location||Study period||Attendance options||Available to|
- International students
- Domestic students
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|Study Period||Start date||Census date||WW date||End date|
* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (see withdrawal dates explained for more information).
Unit census dates currently displaying for 2021 are indicative and subject to change. Finalised census dates for 2021 will be available from the 1st October 2020. Note census date cutoff is 11.59pm AEST (AEDT during October to March).
- Prove and apply a range of standard concepts and results from the probability theory, and give their physical interpretations.
- Observe the patterns in the MATLAB output and interpret them using the physical interpretations, detailing what you observe in the output, what it tells you about the process, and why it makes sense in terms of the dynamics of the underlying process.
- Understand the concept of probability and its properties, and apply the axioms and basic rules, including Chain Rule, Law of Total Probability and Bayes’s rule.
- Apply appropriate discrete/continuous time distributions to solve problems. Give their physical interpretations and derive their properties.
- Calculate probability distribution function given weights of a discrete random variable, and vice versa.
- Calculate probability distribution function given density function of a continuous random variable, and vice versa.
- Calculate probability distribution function of a mixed random variable.
- Apply joint distribution and conditional distribution in solving problems.
- Evaluate and apply probability generating function/Laplace-Stieltjes transform/moment generating function of a given distribution.
- Apply standard limit theorems.
- Define Bernoulli process and give the physical interpretations of corresponding discrete time random variables in terms of its performance measures. Apply it in solving problems.
- Define Poisson process (in two different ways) and give the physical interpretations of corresponding discrete time and continuous time random variables in terms of its performance measures. Apply it in solving problems.
- Define discrete-time Markov Chains (DTMC) and continuous-time Markov Chain (CTMC), and give the physical interpretations of their parameters and performance measures.
- Model and solve a given problem as a DTMC or a CTMC.
- Determine communicating classes, transient/recurrent states of a given DTMC.
- Calculate probability distribution at time n/mean recurrence times/stationary distribution for a given DTMC.
- Construct the corresponding embedded chain from a given CTMC.
- Calculate the steady state distribution for a given CTMC.
- Establish transience or recurrence of states of a CTMC using the embedded chain.
- Apply Kolmogorov Differential Equations for a CTMC.
|Field of Education||Commencing Student Contribution 1||Grandfathered Student Contribution 1||Approved Pathway Course Student Contribution 2||Domestic Full Fee|
- Available as a Commonwealth Supported Place
- HECS-HELP is available on this unit, depending on your eligibility3
- FEE-HELP is available on this unit, depending on your eligibility4
1 Please refer here more information on student contribution amounts.
2 Information on eligibility and Approved Pathway courses can be found here
3 Please refer here for eligibility for HECS-HELP
4 Please refer here for eligibility for FEE-HELP
Please note: international students should refer to this page to get an indicative course cost.
PrerequisitesAny Intermediate unit in Mathematics
|Assessment||Report (10%)|Report (10%)|Report (10%)|Examination - invigilated (externally - Exams Office) (70%)|
|Timetable||View the lecture timetable | View the full unit timetable|
Required readings will be listed in the unit outline prior to the start of classes.
|Links||Booktopia textbook finder|
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