Syllabus academic year 2007/2008

Higher education credits: 9. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in Swedish. FMS012 overlap following cours/es: FMS011, FMS021, FMS022, FMS032, FMS033, FMS035, FMS086, FMS120, FMS121, FMS140, MAS233, FMS011, FMS021, FMS022, FMS032, FMS033, FMS035, FMS086, FMS120, FMS121, FMS140 och MASB03. Compulsory for: C2, D2, E2, F2, I2, N2, Pi2. Course coordinator: Anna Lindgren, Director of studies,, Matematisk statistik. Prerequisites: At least 12 university credits within the courses FMA410, FMA420 or FMA425, and FMA430 or FMA435 or FMA025. Recommended prerequisits: Calculus in one and several variables, Linear algebra, and at least one programme characteristic course with critical examination of observed data. Assessment: Written exam and compulsory computer exercises. Further information: The course is also given for physicists at the faculty of science with the code MAS233. Home page:

The course is intended to give the student the basics in mathematical modelling of random variation and an understanding of the principles behind statistical analysis. It shall also give the students a toolbox containing the most commonly used models and methods, as well as the ability to use these in practical situations. The student shall also be able to handle dependence between observations.

The course fills two purposes, providing a fundamental knowledge of mathematical statistics, as well as giving a foundation for further studies.

The fundamental knowledge is essential for those who, in their professional lives, will not necessarily be involved in statistical analyses on a daily basis, but who, on occasion, will be expected to perform basic statistical tests and present the results for their colleagues. They will also be expected to be able to read and assess the analyses of others.

The main purpose of the course is to provide a basis for further studies. Both in stochastic modelling and analysis of random phenomena in time and/or space, and in the application areas, such as telecommunications, economics, signal processing, logistics, and process control. The focus therefore lies in probability theory and stochastic modelling of both independent and dependent data.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

Data analysis. Descriptive statistics. Axioms of probability. Conditional probability, independent events. Stochastic variables and functions of the same. Expectation, variance, and covariance. Normal distribution, binomial distribution, and other important distributions for measurements and frequencies. Conditional distributions and conditional expectations. Point estimates and their properties. Maximum likelihood and Least squares. Principles of interval estimates and hypothesis testing. Methods for normally distributed observations. Approximative methods based on the normal distribution. Estimates of proportions. Correlation. Linear univariate and multiple regression. Introduction to stochastic processes. Examples are chosen with respect to the different programs.

Blom, G, Enger, J, Englund, G, Grandell, J, Holst, L: Sannolikhetsteori och statistikteori med tillämpningar. Studentlitteratur 2005. ISBN:91-44-02442-8