# PROBABILITY AND STATISTICS - 2023/4

Module code: MAT1033

## Module Overview

This module is an introduction to probability theory and statistical methods.  The module leads to a deeper understanding of probability distributions, random variables and their role in sampling.  Tools such as hypothesis tests are presented and a basic introduction to the statistical software R is provided.  The module lays the foundations for Year 2 Mathematical Statistics (MAT2013), General Linear Models (MAT2002) and Stochastic Processes (MAT2003).  More generally, it underpins other modules where an element of uncertainty/chance/randomness exists or where knowledge of the software package R is required.

### Module provider

Mathematics

KUEH Audrey (Maths)

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

Independent Learning Hours: 97

Lecture Hours: 33

Seminar Hours: 5

Laboratory Hours: 4

Captured Content: 11

Semester 1

None

## Module content

Indicative content includes:

• Probability theory, including  Bayes' Theorem;

• Standard discrete distributions: binomial and Poisson;

• Standard continuous distributions: normal and exponential;

• Expectation, moments, and probability generating functions;

• Sums of random variables;

• Statement of the Central Limit Theorem;

• Sampling distributions;

• Unbiased estimators and biased estimators;

• Hypothesis testing and Chi-square tests;

• 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:

• Ability to interpret and manipulate mathematical statements that use probability notation.

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

• Understanding and application of subject knowledge to calculate probabilities and perform statistical tests.

Thus, the summative assessment for this module consists of:

• One two-hour examination taken at the end of the semester; worth 75% of module mark.

• One in-semester test taken during the semester; worth 25% of module mark.

Formative assessment and feedback

Students receive individual written feedback (or auto-feedback from online tests and quizzes) via a number of marked formative coursework assignments over an 11-week period.  The lecturer also provides verbal group feedback during lectures as well as some verbal individual feedback may be given by a seminar tutor at seminars.  (Occasionally group feedback may be provided online when applicable.)

## Module aims

• Introduce students to probability distributions and hypothesis testing.
• Enable students to determine simple probabilities, conditional probabilities, expectations and variances of univariate discrete/continuous random variables and bivariate discrete random variables.
• Illustrate the application of various hypothesis tests for solving frequently encountered problems in sampling and to enable students to apply such tests to similar situations.

## Learning outcomes

 Attributes Developed 1 Demonstrate understanding of the axioms of probability and popular results that can be proved from these axioms K 2 Quote and apply definitions and theorems of probability theory as well as interpret their meaning KCP 3 Calculate probabilities, be able to choose correct approximating distributions and apply an appropriate test given some hypothesis to be proved/disproved KCPT

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.

• Ensure experience is gained (through demonstration) of the methods used to interpret, understand and solve problems in introductory probability and statistics.

The learning and teaching methods include:

• 3 x 1 hour lectures per week for 11 weeks, including notes worked through on the board (or projector-display) to supplement the Lecture Notes that are provided at the beginning of the semester.This also includes Q&A opportunities for students.

• 1 x 1 hour lab session (once every fortnight for eight weeks) for hands-on learning of the statistical software R or online tests using SurreyLearn with Lab Demonstrators on standby to assist students with their questions.

• 1 x 1 hour seminar (once every fortnight for ten weeks) for guided discussion of solutions to problem sheets (provided to students in advance for completion to reinforce their understanding and guide their learning).

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

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics MMath 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 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 with Music BSc (Hons) 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 2023/4 academic year.