# MATHEMATICAL STATISTICS - 2020/1

Module code: MAT2013

Module Overview

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.

Module provider

Mathematics

Module Leader

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

Module Availability

Semester 2

Prerequisites / Co-requisites

MAT1033 (Probability and Statistics)

Module content

Indicative content includes:

- Review of probability theory and common discrete and continuous distributions.
- Bivariate and multivariate distributions.
- Transformations.
- 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 pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Examination | EXAMINATION | 80 |

School-timetabled exam/test | IN-SEMESTER TEST (50 MINS) | 20 |

Alternative Assessment

N/A

Assessment Strategy

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.

Module aims

- 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.

Learning outcomes

Attributes Developed | ||
---|---|---|

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 |

Attributes Developed

**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

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

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.