Syllabus academic year 2010/2011
(Created 2010-07-25.)
Credits: 7,5. Grading scale: TH. Cycle: G2 (First Cycle). Main field: Technology. Language of instruction: The course will be given in Swedish. FMS140 overlaps following cours/es: FMS012, FMS032, FMS033, FMS035 and FMS086. Compulsory for: W3. Course coordinator: Director of studies Anna Lindgren,, Mathematical Statistics. Prerequisites: At least 6 university credits within the courses FMAA01/FMAA05 or FMA430/FMA435/FMA025. Recommended prerequisits: Calculus in one and several variables and Linear algebra. Assessment: Written exam, home assignments, written project report, and peer assessment of the project report. The course grade is based on the exam grade. Parts: 2. Further information: Cooperative learning in fixed smaller groups under tutelage of teacher, discussion and solving of exercises with constant access to the students' computers, individual work with home assignments, project work in groups of two with Matlab, peer assessment of reports, lectures, and seminars. 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 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 to their colleagues. They will also be expected to be able to read and assess the analyses of others.

The course shall also give a basis for further studies, particularly in design of experiments and risk evaluation.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

The course contains fundamental concepts in probability theory, inference theory, regression analysis, and time series analysis.

In probability theory the concepts used are random variables and distributions for describing variation and random phenomena, often related to applications in environmental statistics. Different distributions, such as binomial, Poisson, normal, exponential, and log normal distributions, are studied and the concept of expectation and variance of a distribution is introduced. Special attention is paid to the normal distribution and its property as a limit distribution. Simulations from the distributions and studies of the models are performed in Matlab. This part constitutes approximately 2/7 of the course.

In inference theory we start with observed data and estimate parameters in simple probability models, and describe the uncertainty of the estimates. Emphasis is placed on the relationship between the model and the reality based problem, as well as the conclusions that can be drawn from observed data. In this analysis we use basic techniques, such as confidence intervals and hypothesis testing. This part constitutes approximately 2/7 of the course.

In regression analysis we study how the relationship between two or more variables can be described. Most often the relationship will be linear. Often in environmental applications one of the variables is a time variable which leads to trend analysis. We study different techniques for comparison and choice between different models for relationships. Environmental data if often dependent and therefore we introduce time series with concepts of trend, season, and noise. Techniques, such as auto-correlation function, are used to describe the dependence. A simple AR(1) model for dependent data is introduced. This part, resting heavily on the use of Matlab, constitutes approximately 3/7 of the course.

Vännman K: Matematisk statistik, andra upplagan. Studentlitteratur 2002. Additional material.


Code: 0108. Name: Examination.
Higher education credits: 6. Grading scale: TH. Assessment: Written exam.

Code: 0208. Name: Project Work.
Higher education credits: 1,5. Grading scale: UG. Assessment: Written report.