MATHEMATICAL STATISTICS - 2020/1
Module code: MAT2013
The module gives a presentation of some fundamental mathematical theory underlying statistics. In particular, it provides the theoretical background for many of the topics introduced in MAT1033 or MAT1038 and for some of the topics that appear in higher level statistics modules.
PRINSLOO Andrea (Maths)
Number of Credits: 15
ECTS Credits: 7.5
Framework: FHEQ Level 5
JACs code: G350
Module cap (Maximum number of students): N/A
Prerequisites / Co-requisites
MAT1033 (Probability and Statistics)
Indicative content includes:
- Review of probability theory and common discrete and continuous distributions.
- Bivariate and multivariate distributions.
- Moments, generating functions and inequalities (including Markov’s inequality, Cauchy-Schwartz inequality, Jensen’s inequality, Chebyshev’s inequality).
- Further discrete and continuous distributions: negative binomial, hypergeometric, multinomial, gamma, beta.
- The multivariate normal distribution.
- Distributions associated with the normal distribution: Chi-square, t and F.
- Proof of the central limit theorem
- Normal theory tests and confidence intervals.
|Assessment type||Unit of assessment||Weighting|
|School-timetabled exam/test||IN-SEMESTER TEST (50 MINS)||20|
The assessment strategy is designed to provide students with the opportunity to demonstrate:
· Analytical ability by solution of unseen problems in the test and exam.
· Subject knowledge through the recall of key definitions, theorems and their proofs.
Thus, the summative assessment for this module consists of:
· One two hour examination at the end of the semester; weighted at 80% of the module mark.
· One in-semester test; weighted at 20% of the module mark.
Formative assessment and feedback
Students receive written feedback via a number of marked unassessed coursework assignments over an 11 week period.
- Enable students to prove the properties of a wide range of discrete and continuous distributions.
- Equip students with the tools and techniques to be able to determine properties of distributions not previously encountered.
- Provide students with an understanding of the theory behind common statistical tests.
|1||Use a range of techniques to obtain the properties of distributions.||KC|
|2||State, derive and use common inequalities.||KC|
|3||State and derive results relating to generating functions.||K|
|4||Demonstrate knowledge and critical understanding of proofs relating to statistical tests.||KCT|
C - Cognitive/analytical
K - Subject knowledge
T - Transferable skills
P - Professional/Practical skills
Overall student workload
Independent Study Hours: 117
Lecture Hours: 33
Methods of Teaching / Learning
The learning and teaching strategy is designed to provide:
- A thorough coverage of properties of discrete and continuous distributions and of the techniques used to derive these properties.
- A comprehensive treatment of the theory behind inequalities, generating functions and statistical tests for the subject knowledge
- Experience in problem solving for the cognitive skills.
The learning and teaching methods include:
- 3 x 1 hour lectures per week x 11 weeks, with printed notes which are augmented during lectures.
- Several pieces of unassessed coursework to give students experience of using techniques introduced in the module and to receive formative feedback.
Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.
Programmes this module appears in
|Mathematics with Statistics BSc (Hons)||2||Compulsory||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics with Statistics MMath||2||Compulsory||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics BSc (Hons)||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics MMath||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics with Music BSc (Hons)||2||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Economics and Mathematics BSc (Hons)||2||Compulsory||A weighted aggregate mark of 40% is required to pass the module|
|Financial Mathematics BSc (Hons)||2||Compulsory||A weighted aggregate mark of 40% is required to pass the module|
Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2020/1 academic year.