Course code Mate2037

Credit points 3

# Mathematical Statistics I

Total Hours in Course81

Number of hours for lectures16

Number of hours for seminars and practical classes16

Independent study hours49

Date of course confirmation18.10.2021

Responsible UnitInstitute of Computer Systems and Data Science

### Course developer

Datoru sistēmu un datu zinātnes institūts

## Laima Bērziņa

Dr. sc.ing.

### Course abstract

The study course gives introduction to the basics of mathematical statistics, emphasizing its importance for studies and application to interpret scientific investigations, experiments and data. Students gain an understanding of statistical methods for obtaining logical conclusions by exploring various kinds of random phenomena. The course covers sampling distributions, and hypothesis testing with emphasis on comparing of mean values and analysis of statistical relationship.

### Learning outcomes and their assessment

After the study course students will have: knowledge and understanding of the classification and basic principles of the choice of mathematical statistical methods according to tasks of the research (laboratory works); skills to apply mathematical statistical methods for course projects and diploma, as well as professional research tasks (laboratory works, tests); competence to analyse, systematize data processing results and use them for environmental engineering studies (independent work).

### Course Content(Calendar)

Full time intramural studies:
1. The role of statistics in environmental engineering,2h.
2. Random variables and probability distributions,2h.
3. Random sampling and data description,2h.
4. Evaluation of population parameters. Statistical hypotheses,2h.
5. Distributional tests. Normal distribution law,2h.
6. t-test for dependent samples,2h.
7. t-test for independent samples and Fisher's F test,2h.
8. Test Nr.1.,2h.
9. Analysis of correlation,2h.
10. Simple linear regression analysis,2h.
11. Basics of nonlinear regression analysis,2h.
12. Multiple linear regression analysis,2h.
13. Design and analysis of single-factor experiments: the analysis of variance,2h.
14. χ2 as a statistical independence test,2h.
15. Non-parametric statistical methods,2h.
16. Test Nr.2.,2h.
Part time extramural studies:
All topics specified for full time studies are accomplished, but the number of contact hours is one half of the number specified in the calendar

### Requirements for awarding credit points

2 tests during the course;
submission of independent work results.

### Description of the organization and tasks of students’ independent work

During the semester the student has to perform independent work. The work must be written and submitted electronically on the e-learning site.

### Criteria for Evaluating Learning Outcomes

Cumulative course grade will be determined during as a average score of 2 tests and evaluation of independent work outcomes.

1. Arhipova I., Bāliņa S. Statistika ekonomikā un biznesā. Rīga: Datorzinību Centrs, 2006. 364 lpp.
2. Smotrovs J. Varbūtību teorija un matemātiskā statistika II. Rīga: Zvaigzne ABC, 2007. 136 lpp.
3. Grīnglazs L., Kopitovs J. Matemātiskā statistika: ar datoru lietojuma paraugiem uzdevumu risināšanai. Rīga: Rīgas Starptautiskās ekonomikas un biznesa administrācijas augstskola, 2003. 310 lpp.
4. Krastiņš O. Ciemiņa I. Statistika. Rīga: LR Centrālā statistikas pārvalde, 2003. 267 lpp.