MATHEMATICAL STATISTICS, BASIC COURSE | FMS012 |

**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 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

- 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, conditional probability, distribution, expectation, variance, and covariance,
- 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, as well as modify them to fit more complicated 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 use a computational program for simulation och interpretation of statistical models, as well as for data analysis,
- be able to choose, modify, perform, and interpret a statistical procedure that answers a given statistical problem,
- be able to use statistical terms within the field in writing.

*Judgement and approach*

For a passing grade the student must

- be able to examine a statistical model and its ability to describe reality.

**Contents**

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.

**Literature**

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