Statistics

2022/2023
Programme:
Practical Mathematics
Year:
2 year
Semester:
second
Kind:
mandatory
ECTS:
5
Language:
slovenian
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
1
Lab
1
Content (Syllabus outline)

Descriptive statistics: mean, standard deviation, covariance.
Graphical representation of data: histograms, charts, QQ-diagrams.Sampling: introductory examples, sampling design, sampling distribution, standard error, confidence interval.Regression models: linear regression model, parameter estimation, prediction, regression models as a research tool.Testing the hypothesis: the basic idea of the test statistics and their distributions, p-values, examples.

Readings

D. Freedman, R. Pisani, R. Purves: Statistics, 3rd Edition, Norton, 2003.
M. Hladnik: Verjetnost in statistika, zapiski s predavanj, Fakulteta za računalništvo in informatiko, 2002.
J. Rice: Mathematical Statistics and Data Analysis, 2nd Edition, Duxbury ress, 1996.
R. Scheaffer, M. Gnanadesikan, A. Watkins, J. A. Witmer: Activity Based Statistics, Springer, 1996.

Objectives and competences

Students will consolidate knowledge of probability theory. They will be able to set up mathematical models and apply them to the actual situations.

Intended learning outcomes

Knowledge and understanding: Statistics is one of the most useful branches of mathematics, because it is an effective data analysis.
Application:Statistics is a useful tool in almost every area where conclusions are based on some data. This applies to both the natural sciences and the other sciences such as economics, insurance, and finance.
Reflection:
The subject consolidates knowledge of probability and strengthens the connections between mathematics and its applications.
Transferable skills:
The ability of mathematical modeling and data analysis using abstract models.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Roman Drnovšek:
DRNOVŠEK, Roman. Spectral inequalities for compact integral operators on Banach function spaces. Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 1992, let. 112, str. 589-598. [COBISS-SI-ID 8169561]
DRNOVŠEK, Roman. On invariant subspaces of Volterra-type operators. Integral equations and operator theory, ISSN 0378-620X, 1997, let. 27, št. 1, str. 1-9. [COBISS-SI-ID 7038553]
DRNOVŠEK, Roman. A generalization of Levinger's theorem to positive kernel operators. Glasgow mathematical journal, ISSN 0017-0895, 2003, vol. 45, part 3, str. 545-555. [COBISS-SI-ID 12825945]
Mihael Perman:
PERMAN, Mihael. An excursion approach to Ray-Knight theorems for perturbed Brownian motion. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 1996, let. 63, str. 67-74. [COBISS-SI-ID 7621465]
PERMAN, Mihael, WERNER, Wendelin. Perturbed Brownian motions. Probability theory and related fields, ISSN 0178-8051, 1997, let. 108, št. 3, str. 357-383. [COBISS-SI-ID 7848537]
KOMELJ, Janez, PERMAN, Mihael. Joint characteristic functions construction via copulas. Insurance. Mathematics & economics, ISSN 0167-6687, 2010, vol. 47, iss. 2, str. 137-143. [COBISS-SI-ID 16242777]