MATHEMATICAL STATISTICS, BASIC COURSE | FMS033 |

**Credits:** 5.
**Grading scale:** TH.
**Compulsory for:** L2.
**Course coordinator:** Anna Lindgren, Director of studies, anna@maths.lth.se, Matematisk statistik.
**Recommended prerequisites:** FMA410 Calculus in One Variable, FMA420 Linear Algebra.
**Assessment:** Written exam. To qualify for a final grade, students must have completed the project.
**Homepage:** http://www.maths.lth.se/matstat/kurser/fms033/.

**Aim***General*

The course objective is to give the students the ability to use and construct models for stochastic phenomena, and to give knowledge of data analysis and basic statistic methods. Particular wheight is given to applications in civil engineering.

*Attitude*

The student shall realize that a statistical approach is necessary when planning studies and in the analysis of measurements. The student shall also regard the computer as a natural tool in the data analysis, as well as in the investigation of different model assumptions.

*Knowledge and skills*

The student shall be able to take a problem from real life and, wifth the aide of a collected data material, to construct a reasonable statistical model. Further, the student shall be able to make a critical appraisal of the model and its ability to describe reality. In particular, the student shall be able to

- from a given problem description, identify the random entities, and, in simpler cases, set up a suitable model, interpret its parameters, and state what entity in the model we want to examine;
- state how the probability of a particular outcome is calculated and, in simpler cases, be able to perform the calculation, and to use the Law of Total Probability and Bayess formula;
- state how the expectation of a random variable i calulated and, in simpler cases, be able to perform the calucation;
- determine whether two events are independent and calculate the distribution for the minimum/maximum of independent variables;
- calculate the expectation and variance of linear combinations of random variables;
- use the Central Limit Theorem and explain its practical importance;
- state a suitable estimator as to tool in answering the specific problem, and be able to calculate the properties of the estimator, e.g. expectation, variance, and (approximative) distribution;
- choose a suitable statistical model (test, confidence interval, prediction interval, etc) and perform the calculations;
- draw conclusions and answer the original problem.

**Contents**

Basic knowledge of probability and statistics. Data analysis. Point and interval estimation. Test of hypotheses. Experimental design. Regression and analysis of variance. Applications: measurement errors and propagation, comparisons between expectations and variances.

**Literature**

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