MATHEMATICAL STATISTICS | FMSF01 |

**Aim**

The course is intended to give the student those parts that are missing in the "högskoleingenjör"-education regarding the basics in mathematical modelling of random variation and understanding of the principles behind statistical analysis, in particular computer analysis of observed data, hypothesis testing, and regression analysis.

*Knowledge and understanding*

For a passing grade the student must

- be able to relate questions regarding random variation and observed data to the concepts of random variables, distributions, and relationships between variables,
- be able to describe fundamental techniques for statistical inference and be able to use them on basic statistical models.

*Skills and abilities*

For a passing grade the student must

- be able to construct a simple statistical model describing a problem based on a real life situation or on a collected data material,
- be able to examine a statistical model and its ability to describe reality,
- be able to use a computational program for simulation and interpretation of statistical models, as well as for data analysis,
- be able to choose, perform, and interpret a statistical procedure that answers a given statistical problem,
- be able to use statistical terms within the field in writing,
- be able to present a statistical analysis in a technical report.

**Contents**

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. Different distributions, such as binomial, Poisson, normal, exponential, and log normal distributions. Simulations from the distributions and studies of the models are performed in Matlab.

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.

**Literature**

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