# MAS1608 : Introduction to Probability & R

• Offered for Year: 2020/21
• Module Leader(s): Dr Tom Nye
• Lecturer: Dr Sarah Heaps
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 2 Credit Value: 20 ECTS Credits: 10

#### 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.

QQ-plot for Normal case. 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

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture91:009:00Synchronous On Line Material
Guided Independent StudyAssessment preparation and completion301:0030:00Completion of In Course Assessment
Structured Guided LearningLecture materials361:0036:00Non-Synchronous Activities
Scheduled Learning And Teaching ActivitiesSmall group teaching91:009:00Present in Person
Structured Guided LearningStructured non-synchronous discussion181:0018:00Non Synchronous Discussion to Support Learning
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study941:0094:00Preparation Time for Lectures, Background Reading, Coursework Review
Total200:00
##### Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Student should consult their individual timetable for up-to-date delivery information.

#### Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

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

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A60In Class Test
##### Other Assessment
Description Semester When Set Percentage Comment
Written exercise2M20N/A
Written exercise2M20N/A
##### Assessment Rationale And Relationship

The course assessments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.