Completed courses Analysis 1 and Analysis 2.
Probability and statistics
2024/2025
Programme:
Interdisciplinary University Study Programme Computer Science and Mathematics
Year:
3 year
Semester:
first and second
Kind:
mandatory
ECTS:
10
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
definition of probability
conditional probability
random variables and vectors
discrete and continuous distributions
expectation
variance, covariance and correlation coefficient
higher moments and order statistics
conditional distribution and conditional expectation
generating functions, moment-generating functions
laws of large numbers
central limit theorem
introduction to statistics
sample statistics and estimators
confidence intervals
testing statistical hypotheses
linear regression
goodness of fit tests
nonparametric tests
Readings
- G. Grimmett, D. Stirzaker: Probability and random processes, 3rd ed., Oxford : Oxford University Press, 2001, 2009.
- M. Hladnik: Verjetnost in statistika : zapiski predavanj, Ljubljana : Fakulteta za računalništvo in informatiko, 2002
- R. Jamnik: Matematična statistika, Ljubljana : Državna založba Slovenije, 1980.
- R. Jamnik: Verjetnostni račun in statistika, Ljubljana : Društvo matematikov, fizikov in astronomov Slovenije, 1986, 1995.
Objectives and competences
Introduction to probability theory and its applications in statistics.
Intended learning outcomes
Understanding of theoretical concepts in various applications. The ability to recognize probabilistic and statistical concepts in other sciences (physics, economics, finance, actuarial science, medicine, biology, industrial statistics).
Learning and teaching methods
Lectures, exercises, homeworks.
Assessment
written examination, theoretical test or oral exam
Lecturer's references
Roman Drnovšek:
DRNOVŠEK, Roman. Triangularizing semigroups of positive operators on an atomic normed Riesz space. Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2000, let. 43, št. 1, str. 43-55. [COBISS-SI-ID 9480281]
DRNOVŠEK, Roman. Common invariant subspaces for collections of operators. Integral equations and operator theory, ISSN 0378-620X, 2001, vol. 39, no. 3, str. 253-266. [COBISS-SI-ID 10597721]
DRNOVŠEK, Roman. An infinite-dimensional generalization of Zenger's lemma. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2012, vol. 388, iss. 2, str. 1233-1238. [COBISS-SI-ID 16214617]
Mihael Perman:
PERMAN, Mihael, WELLNER, Jon A. On the distribution of Brownian areas. Annals of applied probability, ISSN 1050-5164, 1996, let. 6, št. 4, str. 1091-1111. [COBISS-SI-ID 7101017]
PERMAN, Mihael, SENEGAČNIK, Andrej, TUMA, Matija. Semi-Markov models with an application to power-plant reliability analysis. IEEE transactions on reliability, ISSN 0018-9529, 1997, vol. 46, no. 4, str. 526-532. [COBISS-SI-ID 2567707]
PERMAN, Mihael, PITMAN, Jim, YOR, Marc. Size-biased sampling of Poisson processes and excursions. Probability theory and related fields, ISSN 0178-8051, 1992, 92, no. 1, str. 21-39. [COBISS-SI-ID 12236377]
