# MATHEMATICAL STATISTICS - 2021/2

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

KUEH Audrey (Physics)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 111

Seminar Hours: 11

Guided Learning: 11

Captured Content: 17

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
Online Scheduled Summative Class Test ONLINE TEST 20
Examination Online ONLINE EXAM 80

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

## 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.