Undergraduate Course: Probability with Applications (MATH08067)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Credits | 20 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | 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. |
Information for Visiting Students
| Pre-requisites | None |
| 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 |
| No Classes have been defined for this Course |
| First Class |
First class information not currently available |
| 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 |
| Keywords | PwA |
Contacts
| Course organiser | Prof Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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