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## Syllabus for

Academic year
MVE590 - Mathematical statistics
Matematisk statistik

Syllabus adopted 2019-02-20 by Head of Programme (or corresponding)
Owner: TKMAS
4,0 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: English
Application code: 55151
Open for exchange students: No
Only students with the course round in the programme plan

 Module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0119 Examination 2,5c Grading: TH 2,5c 30 May 2020 am J, 19 Aug 2020 am J 0219 Design exercise 1,5c Grading: UG 1,5c

#### In programs

TKMAS MECHANICAL ENGINEERING, Year 2 (compulsory)

Sergey Zuyev

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### Course specific prerequisites

Basic courses in mathematical analysis and linear algebra.

#### Aim

The course covers basic Probability theory and statistics with
emphases on concepts and methods of importance for technology.
The course also introduces elements of Experimental design.

#### Learning outcomes (after completion of the course the student should be able to)

• identify and describe problems arising in technical studies for which the treatment requires use of fundamental concepts and methods from Probability theory and Mathematical Statistics;
• summarise data by deriving summary statistics and use graphical methods for their representation;
• formulate probabillistic models for real-world situations and analyse them with the help of probability tools, e.g., conditional probabulities, random variables, distributions;
• understand the random sampling method to gather representative statistics from a population and know the properties of the corresponding estimators of the mean and of the variance;
• be able to check statistical hypotheses on the values of the mean and the variance for one and two samples;
• study linear dependence between two or multiple variates using the tools of regression analysis, analysis of variance and multiple regression.

#### Content

* Probability:
• Probability measure, events, basic combinatorics.
• Random variables, expectation and variance.
• Main distributions: Binomial, Poisson, Exponential, Normal.
• Central Limit Theorem and Poisson Theorem and their applications.
* Statistics:
• Descriptive statistics.
• Sample mean and variance.
• Estimates: point and interval, sampling.
• Hypotheses testing: one and two-sample tests.
• Regression and correlation, multiple regression.

#### Organisation

The teaching of the course is organised around the following components: lectures on the theory, assisted discussion sessions and computer lab work in the web-based Virtual Learning Environment (VLE). In addition to this, a practical Statistical project will be performed in small groups of 3-5 students. The project mark of each individual student will be the group mark weighed according to the peer review system, so not engaging students are much more likely not to get a passing mark for the group project work even if the overall project mark is passable.

#### Literature

The main source is the Study Guide which is available for browsing and download as a whole or by parts from within the VLE. Also recommended but not compulsory:

Douglas C. Montgomery and George C. Runger. Applied Statistics and Probability for Engineers.  4th ed., Wiley, 2006.

#### Examination including compulsory elements

The grade for the course is based on the results of the two tests performed during the course and the final examination.  Students successfully completed the tests are exempt from the final examination. More details and exact dates are available from the course webpage. A pass mark in the project is also necessary in order to be credited for the course. Students who have not passed the exam or have not completed the project in May will be asked to take the re-sit examination in August and/or submit the outstanding project, respectively.

Page manager Published: Wed 26 Feb 2020.