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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2012/2013
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Probability with Applications (MATH08067)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) Credits20
Home subject areaMathematics Other subject areaNone
Course website None Taught in Gaelic?No
Course descriptionThe aim of this course is to develop the basic theory of probability, covering discrete and continuous topics as well as Markov chains and its various applications. The course will have four lecture theatre-hours per week, with the understanding that one of those or equivalent pro rata is for Example Classes and other reinforcement activities.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Introduction to Linear Algebra (MATH08057) AND Calculus and its Applications (MATH08058)
Co-requisites
Prohibited Combinations Students MUST NOT also be taking Probability (MATH08066) AND Statistics (Year 2) (MATH08051)
Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?No
Course Delivery Information
Delivery period: 2012/13 Semester 2, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Location Activity Description Weeks Monday Tuesday Wednesday Thursday Friday
CentralLectureLecture Theatre 1, Appleton Tower1-11 17:10 - 18:00
CentralLectureLecture Theatre 1, Appleton Tower1-11 17:10 - 18:00
CentralLectureLecture Theatre 1, Appleton Tower1-11 17:10 - 18:00
CentralTutorialCentral1-11 16:10 - 17:00
or 17:10 - 18:00
First Class Week 1, Tuesday, 17:10 - 18:00, Zone: Central. Lecture Theatre 1, Appleton Tower
No Exam Information
Summary of Intended Learning Outcomes
1. Facility in practical calculations of probabilities in elementary problems.
2. To acquire a probabilistic understanding of various processes.
3. The ability to identify appropriate probability models and apply them to solve concrete problems.
4. Understanding basic concepts of and the ability to apply methods from discrete probability such as conditional probability and independence to diverse situations.
5. Understanding of and facility in the basic notions of continuous probability such as expectation and joint distributions.
6. To describe Markov chains and their use in a range of applications.
Assessment Information
Up to 15% coursework; the remainder by examination.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus - Basic concepts, sample spaces, events, probabilities, counting/combinatorics, inclusion-exclusion principle;
- Conditioning and independence, Baye¿s formula, law of total probability;
- Discrete random variables (binomial, poisson, geometric, hypergeometric), expectation, variance, mean, independence;
- Continuous random variables, distributions and densities (uniform, normal and exponential);
- Jointly distributed random variables, joint distribution functions, independence and conditional distributions;
- Covariance, correlation, conditional expectation, moment generating functions;
- Inequalities (Markov, Chebyshev, Chernoff), law of large numbers (strong and weak), central limit theorem;
- Discrete Markov chains, transition matrices, hitting times and absorption probabilities, recurrence and transience (of random walks), convergence to equilibrium, ergodic theorem;
- Birth and death processes, steady states, application to telecom circuits, M/M/1 queque;
- (Time permitting) Introduction to entropy, mutual information and coding.
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
KeywordsPwA
Contacts
Course organiserProf Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk
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© Copyright 2012 The University of Edinburgh - 14 January 2013 4:18 am