Course syllabus

# Matematisk statistik, allmän kurs

Mathematical Statistics, Basic Course

## FMSF50, 7,5 credits, G2 (First Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

Admission requirements:## Reading list

## Contact and other information

Mathematical Statistics, Basic Course

Valid for: 2020/21

Decided by: PLED I

Date of Decision: 2020-04-03

Main field: Technology.

Compulsory for: L2, V3

Language of instruction: The course will be given in Swedish

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, particularly in design of experiments.

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 civil engineering and surveying, 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.

Competences and skills

For a passing grade the student must

- be able to construct a simple statistical model describing a problem based an 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 and its interpretation in a report with two parts, where one is technical and the other a short summary aimed at a layman with limited technical knowledge

Judgement and approach

For a passing grade the student must

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

The course contains fundamental concepts in probability theory, inference theory, and regression analysis.

In probability theory the concepts used are random variables and distributions for describing variation and random phenomena, often related to applications in civil engineering and surveying. Different distributions, such as binomial, Poisson, normal, exponential, and log normal distributions, are studied and the concept of expectation and variance of a distribution is introduced. Special attention is paid to the normal distribution and its property as a limit distribution. Simulations from the distributions and studies of the models are performed in Matlab. Different types of measurement errors and error propagation are studied.

In inference theory we start with observed data and estimate parameters in simple probability models, and describe the uncertainty of the estimates. Emphasis is placed on the relationship between the model and the reality based problem, as well as the conclusions that can be drawn from observed data. In this analysis we use basic techniques, such as confidence intervals and hypothesis testing.

In regression analysis we study how the relationship between two or more variables can be described. Most often the relationship will be linear. Models using indicator variables can occur. We study techniques for comparing and choosing among different models. This part rests heavily on the use of Matlab.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written exam, compulsory computer exercises, project report and computational ability test.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts

Code: 0117. Name: Examination.

Credits: 5,5. Grading scale: TH. Assessment: Written exam.

Code: 0217. Name: Laboratory Work.

Credits: 1,5. Grading scale: UG. Assessment: Computer exercises and written project report.

Code: 0317. Name: Computational Ability Test.

Credits: 0,5. Grading scale: UG. Assessment: Computer based test

- At least 6 university credits within the courses FMAA01/FMAA05 Calculus in one variable and FMAB30/FMAB35 Calculus in several variables

Assumed prior knowledge: Calculus in one and several variables and Linear algebra.

The number of participants is limited to: No

The course overlaps following course/s: FMSF20, FMSF25, FMSF30, FMSF35, FMSF40, FMSF45, MASB03, FMSF55, FMSF70, MASB02, FMSF75, MASA01, FMS032, FMS033

- Vännman K: Matematisk statistik, andra upplagan. Studentlitteratur, 2002.
- Lena Zetterqvist och Johan Lindström: Räkna med variation - Ett arbetsmaterial i sannolikhetslära och statistisk inferens. Studentlitteratur, 2017.

Director of studies: Johan Lindström, studierektor@matstat.lu.se

Course homepage: http://www.maths.lth.se/matstat/kurser/fmsf50/

Further information: Changed course code from FMS032. The course may not be included together with FMSF25.