Matematisk statistik, allmän kurs

Valid for: 2024/25

Faculty: Faculty of Engineering LTH

Decided by: PLED I

Date of Decision: 2024-04-16

Effective: 2024-05-08

Main field: Technology
Depth of study relative to the degree requirements: First cycle, in-depth level of the course cannot be classified

Mandatory for: D3, E3

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 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.

Competences and skills

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.

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.

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

Assessment: Written exam, computer exercises 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.

Modules

Code: 0115. Name: Examination.

Credits: 6.0. Grading scale: TH - (U, 3, 4, 5).
Assessment: Written examination.

Code: 0215. Name: Laboratory Work.

Credits: 1.0. Grading scale: UG - (U, G).
Assessment: Computer exercises.

Code: 0315. Name: Computational Ability Test.

Credits: 0.5. Grading scale: UG - (U, G).
Assessment: Computer based test

Admission requirements:

- FMAA01 Calculus in One Variable or FMAA05 Calculus in One Variable or FMAA50 Calculus or FMAB30 Calculus in Several Variables or FMAB35 Calculus in Several Variables or FMAB70 Calculus in One Variable B2 or FMAF01 Mathematics - Analytic Functions or FMAF05 Mathematics - Systems and Transforms or FMAF10 Applied Mathematics - Linear systems

or

(FMAB50 Calculus in One Variable A2 and FMAB60 Calculus in One Variable A3)

The number of participants is limited to: No

Kursen överlappar följande kurser: FMSF30 FMSF35 FMSF40 FMSF45 MASB03 FMSF50 FMSF55 FMSF70 MASB02 FMSF75 MASA01 FMSF80 MASA02

- Blom, G, Enger, J, Englund, G, Grandell, J, Holst, L: Sannolikhetsteori och statistikteori med tillämpningar. Studentlitteratur, 2017, ISBN: 9789144123561. The seventh edition contains no changes to the content compared to the fifth and sixth editions.
- Matematisk Statistik, Matematikcentrum: Matematisk Statistik kompletterande övningar. KFS, 2006. Exercise book.

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

Course administrator: Susann Nordqvist,
expedition@matstat.lu.se

Teacher: Ted Kronvall,
ted.kronvall@matstat.lu.se

Course homepage: https://www.maths.lu.se/utbildning/civilingenjoersutbildning/matematisk-statistik-paa-civilingenjoersprogram/