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Description
This module aims to continue the study of probability and statistics beyond the basic concepts, to provide further study of probability theory, in particular as it relates to multivariate random variables, and to introduce formal concepts and methods in statistical estimation. It is primarily intended for second year students registered on the undergraduate degree programmes offered by the Department of Statistical Science (including the MASS programmes). It also serves as an optional module for students taking the Mathematics and Statistics stream of the Natural Sciences degree.听For all these students, the academic prerequisites for this module are met through compulsory study earlier in their programme.
Intended Learning Outcomes
- have an understanding of the properties of joint distributions of random variables and be able to derive these properties and manipulate them in straightforward situations;
- recognise the chi-squared,听t and F distributions of statistics defined in terms of normal variables;
- be able to apply the ideas of statistical theory to determine estimators and their properties satisfying a range of estimation criteria.
Applications - As with other core modules in probability and statistics, the material in this module has applications in almost every field of quantitative investigation; the module introduces general-purpose techniques that are applicable in principle to a wide range of real-life situations.
Indicative Content - Joint probability distributions: joint and conditional distributions and moments; serial expectation; multinomial and multivariate normal distributions. Transformation of random variables: distributions; approximation of moments; order statistics; joint probability generating and moment generating functions: properties; sums of independent random variables; Central Limit Theorem. Relations between standard distributions: chi-squared, t and F distributions. Statistical estimation: bias, mean square error, consistency; method of moments, least squares, maximum likelihood, Bayesian inference with conjugate priors in the discrete and continuous settings. Asymptotic properties of maximum likelihood estimators.
Key Texts - Available from .
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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