Mathematical Statistics - MA5507

Location Term Level Credits (ECTS) Current Convenor 2017-18 2018-19
Canterbury Autumn
View Timetable
5 15 (7.5) DR AF Laurence







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 MA348 and MA349. 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, the method of maximum likelihood, is 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; Transformations of random variables; Sampling distributions; Point and interval estimation; Properties of estimators; Maximum likelihood; Hypothesis testing; Neyman-Pearson lemma; Maximum likelihood ratio test.


This module appears in:

Contact hours


Method of assessment

80% Examination, 20% Coursework

Preliminary reading

MILLER, I. and MILLER, M. (2014) John E. Freund's Mathematical Statistics with Applications. 8th international edition. Pearson Education, Prentice Hall, New Jersey.
LINDLEY, D.V. and SCOTT, W.F. (1995) New Cambridge Statistical Tables. 2nd edition.
HOGG, R., CRAIG, A. and McKEAN, J. (2003) Introduction to Mathematical Statistics. 6th international edition.
LARSON, H. J. (1982) Introduction to Probability Theory and Statistical Inference. 3rd edition.
SPIEGEL, M. R, SCHILLER, J. and ALU SRINIVASAN, R. (2013) Schaum's Outline of Probability and Statistics. 4th edition.
LEE, P. M. (2012) [for level 6 students] Bayesian Statistics an Introduction. 4th edition. (ebook)

See the library reading list for this module (Canterbury)

See the library reading list for this module (Medway)

Learning outcomes

8. The intended subject specific learning outcomes.
On successfully completing the level 5 module students will be able to:
8.1 demonstrate knowledge and critical understanding of the well-established principles within probability and inference;
8.2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: joint, marginal and conditional probability distributions, to derive distributions of transformed random variables, to calculate point and interval estimates of parameters and to perform tests of hypotheses;
8.3 apply the concepts and principles in probability and inference in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.

9. The intended generic learning outcomes.
On successfully completing the level 5 module students will be able to:
Demonstrate an increased ability to:
9.1 manage their own learning and make use of appropriate resources;
9.2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
9.3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
9.4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
9.5 solve problems relating to qualitative and quantitative information;
9.6 make use of information technology skills such as online resources (moodle), internet communication;
9.7 communicate technical material competently;

9.8 demonstrate an increased level of skill in numeracy and computation.

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