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. This unit is within the major: Statistics and Decision Science (Bachelor of Science).
|Unit name||Probability Models 3|
|College/School||College of Sciences and Engineering
School of Natural Sciences
|Coordinator||Associate Professor Malgorzata O'Reilly|
|Available as an elective?||Yes|
|Delivered By||University of Tasmania|
|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 (refer to How do I withdraw from a unit? for more information).
Unit census dates currently displaying for 2024 are indicative and subject to change. Finalised census dates for 2024 will be available from the 1st October 2023. Note census date cutoff is 11.59pm AEST (AEDT during October to March).
- Construct probability models for a range of real-world situations.
- Apply analytical techniques from probability theory and models to analyse abstract and real-world problems.
- Use mathematical language and notation to communicate probability theory and stochastic models to peers.
- State and use formal definitions and properties of structures within axiomatic theory of probability in a rigorous manner.
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PrerequisitesAny intermediate level (200 coded) KMA unit
3 x 1-hr lectures, 1 x 1-hr tutorial , 1 x 1-hr lab weekly
|Assessment||Demonstration (10%)|Examination (40%)|Assignment (multiple) (50%)|
|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.
• S. M. Ross, Introduction to Probability Models
|Links||Booktopia textbook finder|
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