# PROBABILITY AND STATISTICS - 2024/5

Module code: MAT1033

## Module Overview

Probability is a numerical description of random events, and statistics is the science of collecting and analysing data from these random events and modelling them with random variables. Students will be introduced to the basic concepts of probability distributions, hypothesis testing and random variables. These concepts are fundamental in probability and statistics and lay the foundations for Level 5 Mathematical Statistics (MAT2013), Linear Statistical Methods (MAT2053) and Stochastic Processes (MAT2003). Students will also be introduced to programming in the statistical software R, and thus gain employability through enhancing their digital capabilities.

### Module provider

Mathematics & Physics

KUEH Audrey (Maths & Phys)

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

Independent Learning Hours: 61

Lecture Hours: 33

Seminar Hours: 5

Laboratory Hours: 3

Guided Learning: 15

Captured Content: 33

Semester 1

None

## Module content

Indicative content includes:

• Probability theory, including Conditional probability;

• Ideal hypothesis testing, Confirmatory data analysis;

• Standard discrete distributions: Uniform, Binomial and Poisson;

• Standard continuous distributions: Uniform, Exponential and Normal;

• Expectation, Variance, Standard deviation;

• Probability generating functions, Moment generating functions;

• Joint probability mass functions, Marginal probability mass functions;

• Statement of the Central Limit Theorem;

• Introduction to the statistical software R.

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-semester test (50 minutes) 25
Examination Exam (2 hours) 75

N/A

## Assessment Strategy

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

• Interpretation and manipulation of mathematical statements that use probability notation.

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

• Analytical ability to calculate probabilities and perform statistical tests.

Thus, the summative assessment for this module consists of:

• One in-semester test taken during the semester, worth 25% of the module mark, corresponds to Learning Outcomes 1, 2, 3.

• A synoptic examination (2 hours), worth 75% of the module mark, corresponds to Learning Outcomes 1, 2, 3.

Formative assessment

There are three 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 two courseworks will assist students with preparation for the in-semester test. The feedback from all three courseworks and the in-semester test will assist students with preparation for the synoptic examination. Students also receive verbal feedback during lectures, seminars and computer lab sessions.

## Module aims

• Introduce students to random variables and enable them to determine means, variances and standard deviations.
• Facilitate students' understanding of various hypothesis tests through applications in frequently encountered problems in sampling.
• Develop the digital capabilities of students by introducing R.
• Introduce students to basic concepts of probability and enable them to calculate simple probabilities and conditional probabilities.
• Give students a thorough understanding of the methodology of hypothesis testing, as well as the strengths and weaknesses of this methodology.

## Learning outcomes

 Attributes Developed 002 Students will be able to quote and apply definitions and theorems of statistics as well as interpret their meaning. KC 003 Students will be able to calculate probabilities, choose correct approximating distributions and apply an appropriate test given some hypothesis to be proved/disproved. KCT 004 Students will gain familiarity in programming through the introduction of R. KCPT 001 Students will understand the axioms of probability and popular results that can be proved from these axioms. K

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 detailed introduction to probability theory, distributions and hypothesis testing and ensure experience in the methods used to interpret, understand and solve problems in introductory probability and 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.

• Three one-hour computer lab sessions in which students gain practical experience of analysing data sets using R.

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

• Three 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: MAT1033

## 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 computer lab sessions in MAT1033 are specifically designed to help students cultivate basic programming skills using the statistical software R.

• Employability: The computer lab sessions are specifically designed to help students cultivate basic programming skills, which are not only useful at the workplace, but also teach students about structuring their thoughts through algorithms.

• Global and Cultural Capabilities: Students enrolled in MAT1033 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: MAT1033 teaches students analytical skills to tackle uncertainty. The statistical proficiency gained from taking the module sharpens their problem-solving abilities. This gives students tools to complete challenging assignments and thus builds their resourcefulness and resilience.

• Sustainability: Students enrolled in MAT1033 learn about hypothesis testing which is used to make data-driven decisions in a vast variety of areas, including management of scarce resources and climate science.

## 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 BSc (Hons) 1 Compulsory 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 Compulsory A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 1 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 2024/5 academic year.