Probability

This subject has the following teaching availabilities in 2009:

Calculus 2 with a grade of H2B or above, plus Linear Algebra;

Or

One of

• Accelerated Mathematics 1 (620-157 Mathematics 1 prior to 2009);
• 620-190 (UMEP Maths for High Achieving Students);

plus Accelerated Mathematics 2 (620-158 Mathematics 2 prior to 2009);

Or

One of

• 620-120 (UMEP Maths for High Achieving Students)(prior to 2008)

• 620-121 (prior to 2008)
• 620-140 (prior to 2008)
• 620-141 (prior to 2008)

plus one of

• 620-113 (prior to 2008)
• 620-123 (prior to 2008)
• 620-131 (prior to 2008)
• 620-143 (prior to 2009) with a grade of H2B or above

• 620-193 (prior to 2006) with a grade of H2B or above

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).

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.

Up to 50 pages of written assignments due during semester (20%); a 3-hour written examination in the examination period (80%).

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

• Bachelor of Arts
• Bachelor of Commerce
• Bachelor of Environments
• Bachelor of Music

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.

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.

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 Probability instead of 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.