Department of Mathematics
Probability Models
Course G1100
Course details for 2010 cohort.
Level 3
15 credits
Autumn term
Course Outline
Probability spaces as models of chance experiments. Axioms, conditional probability. Random variables, distributions, densities, mass functions. Random vectors, joint and marginal distributions, conditioning. Expectation, indicator variables, laws of Large Numbers, moment generating functions, central limit theorem. Ideas of convergence of random variables. Markov chains, including random walk. Poisson processes. The Wiener process.
Learning Outcomes
By the end of the course a successful student should be able to
* set up plausible models of probability spaces for a variety of chance
experiments;
* find probabilities and other properties associated with random
variables and vectors;
* use indicator variables, and the idea of conditional expectation,
appropriately;
* apply the Laws of Large Numbers and the Central Limit Theorem;
* set up transition matrices of Markov Chains, and describe their longterm
behaviour;
* calculate probabilities and expectations relevant to the use of Poisson processes and the Wiener process in modelling appropriate situations.
Pre-Requisite
Probability and Statistics, or equivalent.
Library
Recommended books:
D. Stirzaker, Stochastic Processes and Models.
J.Haigh, Probability Models.
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Summer Term | 80.00% |
| Coursework | 20.00% | |
| Coursework components. Average of best 4 coursework marks. | ||
| Problem Sets | Spring Week 1 | |
| Problem Sets | Autumn Week 4 | |
| Problem Sets | Autumn Week 8 | |
| Problem Sets | Autumn Week 6 | |
| Problem Sets | Autumn Week 10 | |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Autumn Term | LECTURE | 2 hours | 111111111100 |
| Autumn Term | LECTURE | 1 hour | 101010101000 |
| Autumn Term | WORKSHOP | 1 hour | 010101010100 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Omar Lakkis
Assess convenor
http://www.sussex.ac.uk/profiles/173323
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