This module is not currently running in 2024 to 2025.
This module is a pre-requisite for many of the other statistics modules at Stages 2, 3 and 4, but it can equally well be studied as a module in its own right, extending the ideas of probability and statistics met at Stage 1 and providing practice with the mathematical skills learned in MA321. It starts by revising the idea of a probability distribution for one or more random variables and looks at different methods to derive the distribution of a function of random variables. These techniques are then used to prove some of the results underpinning the hypothesis test and confidence interval calculations met at Stage 1, such as for the t-test or the F-test. With these tools to hand, the module moves on to look at how to fit models (probability distributions) to sets of data. A standard technique, known as the method of maximum likelihood, is introduced, which is then used to fit the model to the data to obtain point estimates of the model parameters and to construct hypothesis tests and confidence intervals for these parameters. Outline Syllabus includes: Joint, marginal and conditional distributions of discrete and continuous random variables; Generating functions; Transformations of random variables; Sampling distributions; Point and interval estimation; Properties of estimators; Maximum likelihood; Hypothesis testing; Neyman-Pearson lemma; Maximum likelihood ratio test.
42-48 lectures and example classes/workshops
90% Examination, 10% Coursework
I Miller & M Miller John E Freund’s Mathematical Statistics with Applications, 7th ed., Pearson Education, Prentice Hall, New Jersey, 2003 (QA276).(R)
RV Hogg, JW McKean & AT Craig Introduction to Mathematical Statistics, 6th ed., Prentice Hall, 2003 (QA276) (B)
HJ Larson Introduction to Probability Theory and Statistical Inference. (3rd ed., Wiley, 1982) (HA29)(B)
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes
On successful completion of this module, level 5 students will be able to demonstrate:
a) a reasonable knowledge of probability theory and of the key ideas of statistical inference, in particular to enable them to study further statistics modules at levels I and H (for which this module is a pre-requisite);
b) a reasonable ability to use mathematical techniques to manipulate joint, marginal and conditional probability distributions, and to derive distributions of transformed random variables;
c) a reasonable ability to use mathematical techniques to calculate point and interval estimates of parameters and to perform tests of hypotheses;
d) some appreciation of the relevance of mathematical statistics to real world problems.
On successful completion of this module, level 6 students will also be able to demonstrate:
e) a systematic understanding of the areas of probability theory and frequentist statistics covered by this module, in particular to enable them to study further statistics modules at levels H and M (for which this module is a pre-requisite);
f) an ability to explore the statistical literature to extend their experience in frequentist statistics into the area of Bayesian inference.
12. The intended generic learning outcomes
On successful completion of this module, level 5 students will have:
a) developed their understanding of probability and statistics;
b) applied a range of mathematical techniques to solve statistical problems;
c) developed their ability to abstract the essentials of problems and to formulate them mathematically;
d) improved their key skills in numeracy and problem solving;
e) enhanced their study skills and ability to work with relatively little supervision.
On successful completion of this module, level 6 students will also have:
f) demonstrated an ability to extend their existing knowledge of statistics into new areas through independent study.
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