Probability

Subject MAST20004 (2010)

Note: This is an archived Handbook entry from 2010.

Credit Points: 12.50
Level: 2 (Undergraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2010:

Semester 1, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable

Lectures, practice classes and computer laboratory classes.

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 3 x one hour lectures per week, 1 x one hour practice class per week, and 1 x one hour computer laboratory class per week
Total Time Commitment: Estimated total time commitment of 120 hours
Prerequisites:

One of

and one of

Or

One of

  • 620-121 Mathematics A Advanced (prior to 2008)
  • 620-120 UMEP Maths for High Achieving Students (prior to 2008)
  • 620-140 Intermediate Mathematics (prior to 2008)
  • 620-141 Mathematics A (prior to 2008)

and one of

  • 620-113 Applied Mathematics Advanced Plus (prior to 2008)
  • 620-123 Applied Mathematics Advanced (prior to 2008)
  • 620-143 Applied Mathematics (prior to 2009) with a grade of H2B or above
  • 620-193 Applied Mathematics (prior to 2006) with a grade of H2B or above
  • 620-131 Scientific Programming and Simulation (prior to 2008)
Corequisites: None
Recommended Background Knowledge: None
Non Allowed Subjects:

Students may only gain credit for one of

Core Participation Requirements: It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their active and safe participation in a subject are encouraged to discuss this with the relevant subject coordinator and the Disability Liaison Unit.

Coordinator

Prof Peter Taylor

Contact

Second Year Coordinator

Email: sycoord@ms.unimelb.edu.au

Subject Overview:

This subject offers a thorough grounding in the basic concepts of mathematical probability and probabilistic modelling. Topics covered include random experiments and sample spaces, probability axioms and theorems, discrete and continuous random variables/distributions (including measures of location, spread and shape), expectations and generating functions, independence of random variables and measures of dependence (covariance and correlation), methods for deriving the distributions of transformations of random variables or approximations for them (including the central limit theorem).

The probability distributions and models discussed in the subject arise frequently in real world applications. These include a number of widely used one- and two-dimensional (particularly the bivariate normal) distributions and also fundamental probability models such as Poisson processes and Markov chains.
Objectives:

After completing this subject students should:

  • have a systematic understanding of the basic concepts of probability space, probability distribution, random variable (including the bivariate case) and expectation
  • be able to use conditional expectations, generating functions and other basic techniques taught in the subject;
  • be able to interpret a number of important probabilistic models, including simple random processes such as the Poisson process and finite discrete time Markov chains, and appreciate their relevance to real world problems;
  • be able to formalize simple real-life situations involving uncertainty in the form of standard probabilistic models and to analyse the latter;
  • develop understanding of the relevance of the probabilistic models from the subject to the important areas of applications such as statistics and actuarial studies.
Assessment:

Four written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).
Prescribed Texts: None
Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills:

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time management skills: the ability to meet regular deadlines while balancing competing commitments.
  • computer skills: the ability to use mathematical computing packages.
Notes:

This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.

Students undertaking Actuarial Studies should take 620-201 Probability instead of 620-205 Probability for Statistics.

Students undertaking this subject will regularly use computers in weekly computer classes, with all the necessary software installed.

Students undertaking this subject are not assumed to have any special computer skills at the beginning.
Related Course(s): Bachelor of Science
Related Majors/Minors/Specialisations: Economics Major
Mathematics && Statistics Major

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