# MAS1608 : Introduction to Probability & R

• Offered for Year: 2023/24
• Module Leader(s): Dr Kevin Wilson
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters

Your programme is made up of credits, the total differs on programme to programme.

 Semester 2 Credit Value: 20 ECTS Credits: 10.0 European Credit Transfer System

#### Aims

To develop ideas and methods that are essential for the study of probability and statistics. To develop a familiarity with ideas of discrete and continuous probability models and their interpretation. To develop concepts in probability that underpin methods of statistical inference.

Module summary

The course will cover the key concepts required for further study of probability and statistics. We begin with the fundamentals of probability theory, considering probability for discrete outcomes such as National Lottery draws or poker hands. We will then move on to probability distributions and investigate how they can be used to model uncertain quantities such as the response of patients to a new treatment in a clinical trial and the occurrence of earthquakes in tectonically active regions. The module will introduce ideas of bivariate distribution and covariation, which are fundamental to many of the most useful statistical techniques.

#### Outline Of Syllabus

Introduction to random variation and probability including the probability axioms.

Conditional probability and independence.

Discrete probability models: the binomial, geometric and Poisson distributions. Discrete bivariate models.

Continuous probability models: the uniform, exponential and Normal distributions.

Bivariate continuous distributions.

Use of R for mathematical computing. Getting started, input and output, data types, plotting and simple calculations, control statements, functions, random variables. Use of R for illustration of fundamental concepts in probability.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture111:0011:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture311:0031:00Formal Lectures
Guided Independent StudyAssessment preparation and completion301:0030:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesSmall group teaching51:005:00Group Tutorials
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Computer Cluster Practical Sessions
Guided Independent StudyIndependent study1171:00117:00N/A
Total200:00
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A60N/A
Digital Examination452A20Invigilated test in a cluster
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M20Problem-solving exercises
##### Assessment Rationale And Relationship

A substantial formal unseen written examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

Material on the R programming language is best assessed in a computer-based exam. The coursework assignment allows the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; it has a secondary formative purpose as well as their primary summative purpose.