Mathematical Statistics

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Mathematical Statistics is a sequel to the first-year Probability Theory course. Here we utilise the formal tools of probability distributions to introduce you to the principles of statistical inference. Whereas probability theory can be seen as a branch of deductive mathematics, statistical inference proceeds by inductive reasoning. What this means, in a nutshell, is that general conclusions about entire populations (the "real world") are based on relatively small samples extracted from it (the "data"). It is impossible to make such generalisations without some risk of being wrong. Indeed, much of the “mathematical” content of statistics serves precisely to evaluate and control that risk. The subject matter covered in the course includes random samples and sampling distributions, methods of point estimation, interval estimation and hypothesis testing, the evaluation of these methods in small and large samples, and some applications, with an emphasis on simple linear regression and the bootstrap.