Probability and Statistics
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Description
Probability theory is the branch of mathematics that deals with modelling uncertainty. It is important because of its direct application in areas such as genetics, finance and telecommunications. It also forms the fundamental basis for many other areas in the mathematical sciences including statistics, modern optimisation methods and risk modelling. This course provides an introduction to probability theory, random variables and Markov processes.
Objective
Content
Topics covered are: probability axioms, conditional probability; Bayes' theorem; discrete random variables, moments, bounding probabilities, probability generating functions, standard discrete distributions; continuous random variables, uniform, normal, Cauchy, exponential, gamma and chi-square distributions, transformations, the Poisson process; bivariate distributions, marginal and conditional distributions, independence, covariance and correlation, linear combinations of two random variables, bivariate normal distribution; sequences of independent random variables, the weak law of large numbers, the central limit theorem; definition and properties of a Markov chain and probability transition matrices; methods for solving equilibrium equations, absorbing Markov chains.
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| Year |
Semester |
Level |
Units |
| 2012 |
1 |
2 |
3 |
Delivery
42 hours of lectures and tutorials
Assessment
Ongoing assessment 30%, exam 70%.
Graduate attributes
Linkage past
No past linkages have been noted.
Linkage present
No present linkages have been noted.
Linkage future
This course is not recorded as prequisite for other courses.
Restrictions
None
Recommended text
Wackerley, Mendenhall, and Schaeffer: Mathematical Statistics with Applications, 7th Ed.References: Goodman: Introduction to Stochastic models.
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