Undergraduate Course: Probability with Applications (MATH08067)
|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
|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 theatre-hours per week, with the understanding that one of those or equivalent pro rata is for Example Classes and other reinforcement activities.
- Basic concepts, sample spaces, events, probabilities, counting/combinatorics, inclusion-exclusion 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
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.
|High Demand Course?
Course Delivery Information
|Not being delivered|
| 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.
|Students would be expected to own a copy of:|
A First Course in Probability (8th Edition), Sheldon Ross. ISBN: 9781292024929 £52.99 from Blackwells.
|Graduate Attributes and Skills
|Course organiser||Prof Adri Olde-Daalhuis
Tel: (0131 6)50 5992
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427