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. FMS032 overlaps following cours/es: FMS012, FMS030, FMS033, FMS035, FMS086, FMS140, FMS601 and FMSF01. Compulsory for: L2, V3. Course coordinator: Anna Lindgren, Director of studies,, Mathematical Statistics. Prerequisites: At least 6 university credits within the courses FMAA01/FMAA05 and FMA430/FMA435/FMA025. Recommended prerequisits: Calculus in one and several variables and Linear algebra. Assessment: Written exam, compulsory computer exercises, and a project report. The course grade is based on the exam grade. Parts: 2. Further information: The course may not be included together with FMS601 or FMSF01. 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.

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

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

In probability theory the concepts used are random variables and distributions for describing variation and random phenomena, often related to applications in civil engineering and surveying. 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. Different types of measurement errors and error propagation are studied.

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.

In regression analysis we study how the relationship between two or more variables can be described. Most often the relationship will be linear. Models using indicator variables can occur. We study techniques for comparing and choosing among different models. This part rests heavily on the use of Matlab.

Vännman K: Matematisk statistik, second edition. Studentlitteratur 2002.


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

Code: 0208. Name: Laboratory Work.
Higher education credits: 1,5. Grading scale: UG. Assessment: Computer exercises.