TAMS27 Mathematical Statistics 2007

Study Guide@lith

Valid for year : 2007

TAMS27	Mathematical Statistics, 6 ECTS credits. /Matematisk statistik/ For: BKM C D
	Prel. scheduled hours: 52 Rec. self-study hours: 108
	Area of Education: Science Subject area: Mathematics
	Advancement level (G1, G2, A): G2
	Aim: The course gives an introduction to mathematical modelling of experiments where the outcome is influenced by random factors. It is directed towards topics required for application in computer engineering. By the end of the course, the student should understand basic concepts in probability theory be able to set up relevant probability models for random experiments apply the techniques in the course to analyse these models recognise some basic queueing models and some of their applications in telecommunications. understand basic concepts in probability theory, be able to set up relevant probability models for random experiments and apply the techniques in the course to analyse these models. The course finishes with an introduction to basic queueing models and discussion of some applications in telecommunications.
	Prerequisites: (valid for students admitted to programmes within which the course is offered) Series, Integral calculus (one and two variables), Linear algebra, differential calculus. Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
	Supplementary courses: The course prepares the student for: TAMS08, which discusses some of the statistical theory necessary to analyse data using probability models. TAMS47, which develops the theory and applications of stochastic processes. NMAC22 (Markov Chains and Queueing Theory) which develops the queueing models and their applications. TAMS22 (Bayesian Networks) which discusses graphical modelling and algorithms for updating probabilities in causal networks.
	Organisation: Teaching consists of lectures and exercise sessions.
	Course contents: Sample space, events and probabilities. Elementary combinatorial probability. Conditional probability and independence. Discrete random variables and probability distributions, expectation and variance. Binomial, Poisson distributions etc. Probability Generating Function. Continuous Random Variables. Uniform, Exponential and Normal Distributions. Functions of random variables. Moment Generating Function. Simulating a Random Variable. Sampling. The Law of Large Numbers. The Central Limit Theorem. Stochastic Processes: The Poisson Process, introduction to Markov Processes, Birth and death processes, Basic Markov queueing models.
	Course literature: Compendium containing lectures, examples, collection of formulae and tables (required). G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst: Sannolikhetsteori och statistikteori med tillämpningar. (recommended).
	Examination:
	Written examination Computer based and written excercises.	- p - p	/ /	5 ECTS 1 ECTS


Course language is Swedish/English. Department offering the course: MAI. Director of Studies: Eva Enqvist Examiner: John Noble Link to the course homepage at the department Course Syllabus in Swedish

Linköping Institute of Technology
Contact: TFK , val@tfk.liu.se Last updated: 09/26/2008