Department:Mathematics and Statistics
Level:Part II (yr 2)
Course Convenor:Dr JC Whittaker
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Prior to MATH230, the student must have successfully completed:
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CMod descriptionback to top
Events and the axioms of probability. Conditional
probabilities, independence, Bayes' theorem. Discrete random variables.
Standard distributions. Bivariate distributions. Expectations: means,
variances, correlation. Continuous random variables. Transformations of
random variables, simulation of random variables.
Curriculum Design: Outline Syllabusback to top
- Review of basic results in discrete probability.
- Continuous random variables, probability distribution functions, cumulative distribution functions. Expectation and variance of continuous distributions. Higher order moments, skewness and kurtosis.
- Standard distributions: uniform, exponential, gamma, normal, chi-squared, and their inter-relationships and justification as probability models.
- Joint distribution of vector random variables; that is, systems of two or more random variables, marginal and conditional distributions. Expectations and variances of vector variables.
- Properties of linear combinations of random variables.
- Transformations of random variables: motivation, univariate and bivariate methods.
- Limit theory: convergence of variables, laws of large numbers, Central Limit Theorem.
- The Poisson process.
- Multivariate normal distribution.
Educational Aims: Subject Specific: Knowledge, Understanding and Skillsback to top
This course gives a formal introduction to probability and random variables. In the first half we introduce methods for dealing with continuous random variables, building on the work in MATH104 Probability for discrete distributions. We shall use many examples from a variety of statistical applications to illustrate the theoretical ideas.
The second half aims to extend knowledge of probability and distribution theory so that the student should become competent in manipulating functions of one or more random variables, develop probability models for more realistic problems, and discover how distributions that are important in statistical inference are interlinked.