# MATHEMATICAL STATISTICS - 2024/5

Module code: MAT2013

## Module Overview

Statistics is the science of collecting and analysing data from random events and modelling them using random variables. This module first recaps the properties of a single random variable as seen in Level 4 Probability and Statistics (MAT1033), then builds on this by considering multiple random variables simultaneously. This module also covers the transformation of random variables, as well as applications such as tail probabilities and limit theorems.

### Module provider

Mathematics & Physics

KUEH Audrey (Maths & Phys)

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

Independent Learning Hours: 58

Lecture Hours: 33

Tutorial Hours: 11

Guided Learning: 15

Captured Content: 33

Semester 1

N/A

## Module content

Indicative content includes:

• Expectations of functions of univariate and multivariate random variables, including mean, variance, generating functions;

• Standard univariate distributions: Binomial, Chi-square, Continuous Uniform, Discrete Uniform, F, Gamma, Geometric, Poisson, t, Normal;

• Multivariate Normal distribution;

• Univariate and multivariate transformations;

• Derivation and applications of Markov’s inequality, Chebyshev’s inequality, Chernoff’s inequality;

• Derivation and applications of Weak Law of Large Numbers and Central Limit Theorem.

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-semester test (50 minutes) 20
Examination Exam (2 hours) 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Understanding, interpretation and manipulation of statistical statements.

• Subject knowledge through implicit recall of key definitions, theorems and their proofs.

• Analytical ability to deal with unseen distributions in the test and exam.

Thus, the summative assessment for this module consists of:

• One in-semester test taken during the semester, worth 20% of the module mark, corresponds to Learning Outcome 1, 2, 3.

• A synoptic examination (2 hours), worth 80% of the module mark, corresponds to Learning Outcomes 1, 2, 3, 4, 5.

Formative assessment

There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning.

Feedback

Individual written feedback is provided to students for formative unassessed courseworks. The feedback is timed such that feedback from the first coursework will assist students with preparation for the in-semester test. The feedback from both courseworks and the in-semester test will assist students with preparation for the synoptic examination. Students also receive verbal feedback during lectures and tutorials.

## Module aims

• Extend students' understanding of random variables by studying their properties in a formal way.
• Introduce students to useful families of random variables.
• Equip students with the tools to deal with multiple random variables at the same time.
• Give students the basic techniques to transform random variables.
• Introduce students to more advanced topics such as tail probabilities and limit theorems.

## Learning outcomes

 Attributes Developed 001 Students will understand random variables and be able to state, prove and apply main theorems, including (but not limited to) formulae relating to the generating functions and moments. KCT 002 Students will be able to state, prove and apply theorems and formulae relating to the transformation of random variables. KC 003 Students will understand tail probabilities and be able to quote, prove and apply theorems such as Markov's inequality. KCT 004 Students will be able to state and prove limit theorems such as the Central Limit Theorem. KC 005 Students will understand the multivariate normal distribution and other related distributions. KC

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:

Give a thorough treatment of univariate and multivariate random variables, transformations of random variables, tail probabilities and limit theorems and ensure experience in the methods to interpret, understand and solve problems in statistics.

The learning and teaching methods include:

• Three one-hour lectures per week for eleven weeks, with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.

• Eleven tutorials for guided discussion of solutions to problem sheets (provided to students in advance for completion to reinforce their understanding and guide their learning).

• Two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

• Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students the opportunity to review parts of lectures that they may not fully have understood and should not be seen as an alternative to attending lectures.

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.

Upon accessing the reading list, please search for the module using the module code: MAT2013

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourcefulness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

• Digital Capabilities: The SurreyLearn page for MAT2013 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies and facilitates collaborative learning and information sharing.

• Employability: The module MAT2013 equips students with skills which significantly enhance their employability. Students gain mathematical proficiency, which hones critical thinking and problem-solving abilities. Students learn to evaluate complex problems, break them into manageable components, and apply logical reasoning to arrive at solutions — these are highly sought after skills in any profession.

• Global and Cultural Capabilities: Students enrolled in MAT2013 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in tutorials and lectures, which naturally facilitates the sharing of different cultures.

• Resourcefulness and Resilience: MAT2013 is a module which demands a rigorous approach to statistics, to which students will learn to adapt. They will gain skills in analysing problems and lateral thinking. Students will complete assessments which challenge them and build resilience.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Optional 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 2024/5 academic year.