MATH 332/432: STOCHASTIC PROCESSES Amanda Turner B54 Fylde College Department of Mathematics and Statistics Lancaster University Email: a.g.turner@lancaster.ac.uk Telephone: (01524) 593948 Michaelmas 2017
Subject specific aims: The course aims to show how the rules of probability can be used to formulate simple models describing processes, such as the length of a queue, which can change in a random manner, and how the properties of the processes, such as the mean queue size, can be deduced. By the end of the course you should have a good understanding of how probability generating functions can be used to solve many of the model equations, and of the basic theory of Markov chains which underlies many of the process models.
General transferable aims: This course aims to show how stochastic processes can be used to model real-life senarios such as queues, and how such models can be used to aid decisions such as the number of servers for a queue.
Organisation and Assessment
Work is to be submitted by Wednesday 13:00 (quiz to be submitted online, coursework to tutor’s pigeonhole). Solutions will be posted as pdf files on Moodle. Marks for missed deadlines will be penalised by of the maximum possible mark. Work submitted after the solutions have been made available will score zero.
Office hour: 15:00 Tuesdays in Fylde B54.
Assessment: 10% coursework, based on four coursework and four quiz assignments, and 90% from final examination, for which the maximum possible mark is 100.
Examinations: For MATH332, the examination contains Section A and Section B questions. Section A consists of questions worth a total of 40 marks all of which must be attempted; Section B consists of two questions from a choice of three, each worth 30 marks, so that each student can gain at most 60 marks from Section B.
For MATH432, the examination consists of 3 questions worth 100 marks, all of which are compulsory. The level of difficulty is comparable to Section B questions in third year examinations.
Past exam papers are available on the Moodle Mathematics Information pages.
Calculators: For the examination, you will be issued with a standard Casio FX-85GT PLUS Scientific Calculator; this will be provided in the examination venue before the start of the exam. If you would like to familiarise yourself with this model, sample calculators may be tried out in the department office. Personal calculators are not permitted for Mathematics and Statistics examinations.
Books
D.R. Cox and H.D. Miller, The Theory of Stochastic Processes, Chapman and Hall, 1965.
G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes (second edition), Clarendon, 1992.
G.R. Grimmett and D. Welsh, Probability: An Introduction, Oxford, 1988.
J.R. Norris, Markov Chains, Cambridge University Press, 1997.
S.M. Ross, An Introduction to Probability Models, Academic Press, 2007.