MAS3901 : Applied Probability
- Offered for Year: 2019/20
- Module Leader(s): Dr Phil Ansell
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 1 Credit Value:||10|
To develop skills in probabilistic reasoning and to gain familiarity with some of the main techniques involved in the analysis of random systems. To develop skills in the analysis of a variety of simple queues.
How can we predict the chance of a gambler winning given a certain strategy? On average how much will they win? Uncertainty is a central feature of almost every real‐life problem, and questions of this nature arise naturally in many applications ranging from economics and finance through to engineering, sports betting and queues. In the first part of this course, we shall discover how certain probabilistic techniques can be used to model and analyse systems or phenomena that evolve randomly over time. In the second part of the course, we will look in detail at the analysis of queues. Queues occur in many situations. For example in telecommunications, traffic engineering, computing and in the design of factories, shops and hospitals all of which are subject to congestion. We will discuss how we construct and analyse models for systems of queues. Crucial questions are how congested any such system is likely to become over time and how we design such systems optimally.
Outline Of Syllabus
Review of probability ideas: conditioning arguments. Gambler's ruin problems, random walks. Markov chains: definition and examples, Chapman‐Kolmogorov equations, classification of states, notions of transience and recurrence, stationary distributions, simulation. Components of a queue; Poisson process; the M/M/1 queue; Birth-Death models; the M/M/c system; optimum number of servers; embedded Markov process; the M/G/1 queue; priority queues, acyclic queuing networks.
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Class tests|
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen exam|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen exam|
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||24||1:00||24:00||Formal lectures|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||12||0:10||2:00||Office hours|
|Guided Independent Study||Independent study||1||19:00||19:00||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||3||3:00||9:00||Review of tests and group project|
|Guided Independent Study||Independent study||1||12:00||12:00||Preparation for group project|
|Guided Independent Study||Independent study||2||6:00||12:00||Revision for class tests|
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: 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.
The format of resits will be determined by the Board of Examiners
|Written Examination||40||1||M||5||2 Class tests (test 1: 2%, test 2: 3%)|
|Prob solv exercises||1||M||5||Group Project|
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The tests and the group project 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.