Probability (MAST20004)

Undergraduate level 2Points: 12.5On Campus (Parkville)

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Overview

Availability
Semester 1
Semester 2
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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.

Intended learning outcomes

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.

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.

Last updated: 14 March 2025

Eligibility and requirements

Prerequisites

One of

Code Name Teaching period Credit Points
MAST10006 Calculus 2
Semester 1 (On Campus - Parkville)
Summer Term (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
 12.5
MAST10021 Calculus 2: Advanced
Semester 2 (On Campus - Parkville)
 12.5
MAST10009 Accelerated Mathematics 2
Semester 2 (On Campus - Parkville)
 12.5

MAST10019 Calculus Extension Studies

IMPORTANT: MAST10006, MAST10021 and MAST10019 must be completed with a mark of at least 60 to count as prerequisites for this subject.

AND

One of

Code Name Teaching period Credit Points
MAST10007 Linear Algebra
Summer Term (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
 12.5
MAST10008 Accelerated Mathematics 1
Semester 1 (On Campus - Parkville)
 12.5
MAST10022 Linear Algebra: Advanced
Semester 1 (On Campus - Parkville)
 12.5

MAST10018 Linear Algebra Extension Studies

MAST10013 UMEP Mathematics for High Achieving Students

Corequisites

None

Non-allowed subjects

Code Name Teaching period Credit Points
MAST20006 Probability for Statistics
Semester 1 (On Campus - Parkville)
 12.5

MAST30015 Statistics for Mechanical Engineers (prior to 2011)

ELEN30002 Stochastic Signals and Systems (prior to 2011)

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 14 March 2025

Assessment

Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS

DescriptionTimingPercentage

Four written assignments due at regular intervals amounting to a total of up to 50 pages

  • 50 pages
During the teaching period20%

A written examination

  • 3 hours
During the examination period80%

Last updated: 14 March 2025

Dates & times

  • Semester 1
    Principal coordinatorMark Fackrell
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 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 commitment170 hours
    Teaching period 2 March 2020 to 7 June 2020
    Last self-enrol date13 March 2020
    Census date30 April 2020
    Last date to withdraw without fail 5 June 2020
    Assessment period ends 3 July 2020

    Semester 1 contact information

    Email: fackrell@unimelb.edu.au

  • Semester 2
    CoordinatorXi Geng
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 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 commitment170 hours
    Teaching period 3 August 2020 to 1 November 2020
    Last self-enrol date14 August 2020
    Census date21 September 2020
    Last date to withdraw without fail16 October 2020
    Assessment period ends27 November 2020

    Semester 2 contact information

    xi.geng@unimelb.edu.au

Time commitment details

Estimated total time commitment of 170 hours

Last updated: 14 March 2025

Further information

Last updated: 14 March 2025