(Created 2011-09-01.)

MATHEMATICAL STATISTICS, BASIC COURSE | FMS035 |

**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 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, both in probability theory and inference theory, as well as in the application areas, such as design of experiments, automatic control, process control, and logistics.

*Knowledge and understanding*

For a passing grade the student must

- be able to relate questions regarding random variation and observed data, as they appear in applications in mechanical engineering, 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,
- understand the a statistical relationship between two variables does not necessarily imply couse-effect.

*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, 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,
- be able to examine a simple measurement situation and judge whether data is collected in a way that allows further analysis.

**Contents**

Expectation and variance. Normal distribution, binomial distribution, and other important distributions for measurements and frequencies. Data analysis. Statistical inference: Point estimates, interval estimates, and hypothesis testing. Methods for normally distributed observations. Approximative methods based on the normal distribution. Comparisons between expectations, variability, and distributions. Estimates of proportions. Regression analysis and calibration. Correlation between two explanatory variables. Examples are chosen with respect to mechanical engineering.

**Literature**

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

**Code: **0112.
**Name: **Examination.

**Higher education credits: ** 6.
**Grading scale: **TH.
**Assessment:** Written exam.

**Code: **0212.
**Name: **Laboratory Work.

**Higher education credits: ** 1,5.
**Grading scale: **UG.
**Assessment:** Computer exercises.