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Mathematical Statistics

Course developer

Course abstract

The aim of the course is to provide students with a theoretical understanding of the basic concepts of probability theory and mathematical statistics with demonstrations of practical application of theory. The main emphasis is on the principles of practical research, professional evaluation and interpretation of intermediate and final results of calculations. In this course, a lot of attention is paid to probability distributions and their characteristics, random variables in engineering.

Learning outcomes and their assessment

Knowledge - able to demonstrate basic and specialized knowledge specific to the field of mathematics and a critical understanding of this knowledge; able to demonstrate understanding of probability distributions and their characteristics, random variables in engineering sciences; (laboratory work)
Skills - using the acquired theoretical knowledge and skills, can formulate and analytically describe information, problems and solutions in the field of mathematical statistics, explain and reasonably discuss these topics with both specialists and non-specialists and use the freely available R program for data processing (laboratory works).
Competencies - able to independently obtain, select and analyze information and use it, make decisions and solve problems in mathematical statistics; able to conduct practical research, analyze the intermediate result, professionally evaluate and interpret the final result.

Course Content(Calendar)

1. Basic concepts of probability theory. Definitions of probability (classical, statistical) (2 h).
2. The simplest operations with probabilities. (2 h).
3. Low of total probability and Bayes theorem. (4 h).
4. Discrete and continuous variables (2h).
5. Numerical characteristics of random variables (2 h).
6. Discrete and continuous distributions (Binomial, Poisson and normal distribution) (4h).
7. Application of statistics in scientific-research work (2 h).
8. 1. test (1 h).
9. Descriptive statistics (2 h).
10. Hypothesis testing (4 h).
11. Parametric methods of analysis of two sample sets (2 h).
12. Non-parametric methods of analysis of two sample sets (2 h).
13. 2. test (1h).

Requirements for awarding credit points

completed and credited laboratory works;
two tests have been written

Description of the organization and tasks of students’ independent work

During the semester, students solve tasks independently. The results are presented in writing and submitted in the e-study environment.

Criteria for Evaluating Learning Outcomes

Test 1 (5 points)
Test 2 (5 points)

At least 2 points must be obtained in each of the tests

Compulsory reading

1.Arhipova I. Varbūtību teorijas un matemātiskās statistikas pielietojumi inženierzinātnēs: mācību līdzeklis. Jelgava: LLU, 2008. 125 lpp.
2.Buiķis M., Carkovs I., Siliņa B. Varbūtību teorijas un statistikas elementi. Rīga: Zvaigzne ABC, 1997. 107 lpp.
3.Krastiņš O., Ciemiņa I. Matemātiskā statistika: mācību grāmata. Rīga: LR Centrālā statistikas pārvalde, 2003. 267 lpp.
4. Hahn Gerald J., Shapiro Samuel S. Statistical Models in Engineering. A Wiley-Interscience Publication. John Wiley & Sons: INC, 1994. 560 p.
5. Robert I. Kabacoff R in Action Data analysis and graphics with R, Manning Publications. Co, 2015, 450 p

Further reading

1.Levine D. M., Ramsey P. P., Smitd R. K. Applied statistics for Engineers and Scientist: Using Microsoft Excel and MINITAB. Upper Saddle River, New Jersey: Prentice Hall, 2001. 671 p.
2.Sprent P., Smeeton N.C. Applied nonparametric statistical methods. Boca Raton, London, New York, Washington D.C.: Chapman Hall/CRC, 2000. 461 p.

Notes

Compulsory course in the ITF bachelor study program "Information Technology for Sustainable Development" and "Computer Control and Computer Science".