Undergraduate

modules

Modules

MAS1604 : Introduction to Probability

Semesters
Semester 2 Credit Value: 15
ECTS Credits: 8.0

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.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture31:003:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture341:0034:00Formal lectures
Guided Independent StudyAssessment preparation and completion19:009:00Revision for class test
Guided Independent StudyAssessment preparation and completion119:0019:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:302:30Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Assignment laboratory
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Guided Independent StudyIndependent study134:3034:30Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study53:0015:00Review of coursework assignments and course test
Guided Independent StudyIndependent study46:0024:00Preparation for coursework assignments
Total150:00
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. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1502A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M10Coursework assignments
Prob solv exercises2M10Coursework test
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of one written assignment (approximately 3%), one assignment laboratory (approximately 3%) and two computer based assessments (each approximately 2%). The coursework assignments and the (in class) coursework test 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 are thus formative as well as summative assessments.

Reading Lists

Timetable