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. Marks on this module can count towards exemption from the professional examination CT3 of the Institute and Faculty of Actuaries. It starts by revising the idea of a probability distribution for one or more random variables, and then 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. Linear regression and analysis of variance models are introduced, which aim to describe the relationship between a random variable of interest and one or more covariates, for example the relationship between income and education level or gender. Outline Syllabus includes: Joint, marginal and conditional distributions of discrete and continuous random variables; Generating functions; Transformations of random variables; Poisson processes; Sampling distributions; Point and interval estimation; Properties of estimators; Maximum likelihood; Hypothesis testing; Neyman-Pearson lemma; Maximum likelihood ratio test; Simple linear regression: ANOVA.
Marks on this module can count towards exemption from the professional examination CT3 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.
approximately 36 scheduled lecture hours; plus 6 workshops.
90% by a 2-hour written examination at the end of the year and 10% coursework.
Students are provided with study notes published be the Actuarial Education Company.
I Miller & M Miller John E Freund’s Mathematical Statistics with Applications, 8th ed. Pearson Education, 2012 (QA276) (R)
RV Hogg, JW McKean & AT Craig Introduction to Mathematical Statistics, 7th ed. Boston, Pearson, 2013 (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 the module, students:
a) will have 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) will have a reasonable ability to use mathematical techniques to manipulate joint, marginal and conditional probability distributions, and to derive distributions of transformed random variables;
c) will have a reasonable ability to use mathematical techniques to calculate point and interval estimates of parameters and to perform tests of hypotheses;
d) will have some appreciation of the relevance of mathematical statistics to real world problems.
The intended generic learning outcomes. On successful completion of the module, students:
a) will have developed their understanding of probability and statistics;
b) will have applied a range of mathematical techniques to solve statistical problems;
c) will have developed their ability to abstract the essentials of problems and to formulate them mathematically;
d) will have improved their key skills in numeracy and problem solving;
e) will have enhanced their study skills and ability to work with relatively little supervision.
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