Undergraduate Course: Probability with Applications (MATH08067)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  The 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 theatrehours per week, with the understanding that one of those or equivalent pro rata is for Example Classes and other reinforcement activities. 
Course description 
 Basic concepts, sample spaces, events, probabilities, counting/combinatorics, inclusionexclusion principle;
 Conditioning and independence, Bayes' 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 queue;
 (Time permitting) Introduction to entropy, mutual information and coding.

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
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.

Reading List
Students would be expected to own a copy of:
A First Course in Probability (8th Edition), Sheldon Ross. ISBN: 9781292024929 £52.99 from Blackwells. 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  PwA 
Contacts
Course organiser  Prof Adri OldeDaalhuis
Tel: (0131 6)50 5992
Email: A.OldeDaalhuis@ed.ac.uk 
Course secretary  Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk 

