MATHEMATICAL STATISTICS | FMS086 |

**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 emphasis lies on models and methods for analysis of experimental data and measurement errors.

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 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.

The course shall also give a basis for further studies, particularly in design of experiments and methods for multidimensional data (Chemometrics).

*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 from a given distribution,
- be able to describe fundamental techniques for statistical inference and be able to use them on basic statistical models,
- be able to explain the purpose and principles of experimental design.

*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 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.

*Judgement and approach*

For a passing grade the student must

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

**Contents**

The basis in probability theory and inference, confidence intervals, statistical methods such as design of experiments and regression analysis. Applications: measurement value analysis, different types of errors and their propagation; comparisons of means and variations; concepts and methods for quality control, estimations of proportions; regression analysis, calibration; factorial designs, optimization of experimental parameters, response surfaces. Applications in chemical and biotechnical engineering are of particular interest.

**Literature**

Olbjer, L: Experimentell och industriell statistik. Lund 2000.

**Code: **0105.
**Name: **Project Work.

**Higher education credits: ** 1,5.
**Grading scale: **UG.
**Assessment:** Written report.
**Contents:** Application of statistical methods on a relevant problem.

**Code: **0205.
**Name: **Examination.

**Higher education credits: ** 6.
**Grading scale: **TH.
**Assessment:** Written exam.
**Contents:** See course contents.