(Created 2008-07-17.)

MATHEMATICAL STATISTICS | FMS601 |

**Aim**

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 fundamental knowledge is essential to 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.

*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 explain the concepts of independence, probability, distribution, expectation, and variance,
- be able to calculate the probability of an event, and the expectation and variance from a given distribution,
- 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 choose, perform, and interpret a statistical procedure that answers a given statistical problem,
- be able to use statistical terms within the field in writing.

**Contents**

Descriptive statistics. Axoims of probability, conditional probability, independent events. Stochastic variables, expectation, and variance. Normal distribution, binomial distribution, and other important distributions. Functions of stochastic variables. Point estimates, interval estimates, hypothesis testing. Methods for normally distributed data. Linear regression.

**Literature**

Vännman, K.: Matematisk statistik. Studentlitteratur, 2 uppl. 2001. ISBN: 91-44-01690-5.