Probability for Statistics

This subject has the following teaching availabilities in 2009:

• 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)

• 620-193 (prior to 2006)

Or

Calculus 2 plus Linear Algebra

This subject develops the probability theory that is necessary to understand statistical inference. Properties of probability are reviewed, random variables are introduced, and their properties are developed and illustrated through common univariate probability models. Models for the joint behaviour of random variables are introduced, along with conditional probability and Markov chains. Methods for obtaining the distributions of functions of random variables are considered along with techniques to obtain the exact and approximate distributions of sums of random variables. These methods will be illustrated through some well known normal approximations to discrete distributions and by obtaining the exact and approximate distributions of some commonly used statistics. Computer packages are used for numerical and theoretical calculations but no programming skills are required.

At the completion of the subject, students are expected to:

• Develop a systematic understanding of probability, random variables, probability distributions and probability models, and their relevance to statistical inference;
• Be able to formulate standard probability models from real world applications and critically assess them;
• Be able to apply the properties of probability distributions, moment generating functions, variable transformations and conditional expectations to analyse common random variables and probability models;
• Be able to use a computer package to perform algebraic and computational tasks in probability analyses.

Up to 50 pages of written assignments due during the semester (20%); a 45-minute computer laboratory test held during the semester (10%); a 3-hour written examination in the examination period (70%).

Hogg and Tanis, Probability and Statistical Inference. Seventh Edition, Prentice Hall, 2005.

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 should progressively acquire generic skills from this subject 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.
• Become familiar with a major statistical computing package.

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 taking this subject must achieve a mark of H2B or above in the subject to proceed to Stochastic Modelling.

Students undertaking this subject are required to regularly use computers with the computer algebra system Maple and statistics package R installed.

Students undertaking this subject are not assumed to have any special computer skills at the beginning. They will learn the basic skills of using Maple in the subject.