Courses & Units

Probability Models 3 KMA305

Introduction

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).

Summary

Unit name	Probability Models 3
Unit code	KMA305
Credit points	12.5
College/School	College of Sciences and Engineering School of Natural Sciences
Discipline	Mathematics
Coordinator	Associate Professor Malgorzata O'Reilly
Available as an elective?	Yes
Delivered By	University of Tasmania
Level	Advanced

Availability

Location	Study period	Attendance options		Available to
Hobart	Semester 1	On-Campus		International	Domestic

Key

: On-campus
: Off-Campus
: International students
: Domestic students

Note

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Key Dates

Study Period	Start date	Census date	WW date	End date
Semester 1	26/2/2024	22/3/2024	15/4/2024	2/6/2024

* 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).

About Census Dates

Learning Outcomes

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.

Fee Information

The 2024 Commonwealth Supported Place (CSP) rates are still being finalised by the Government and we will update the domestic fee information as soon as we have more details.

Requisites

Prerequisites

Any intermediate level (200 coded) KMA unit

Teaching

Teaching Pattern	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

Textbooks

Required	Required readings will be listed in the unit outline prior to the start of classes.
Recommended	• S. M. Ross, Introduction to Probability Models • G. Grimmett and D. Stirzaker, Probability and Random Processes • S. K. Karlin, A First Course in Stochastic Processes • W. Feller, An Introduction to Probability Theory and Its Applications, vol. I • Qi-Ming He, Fundamentals of matrix-analytic methods.
Links	Booktopia textbook finder

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