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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.
Intended learning outcomes
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.
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 statistical computing packages.
Last updated: 7 September 2023