Basic combinatorics.
Outcome space, events, probability.
Conditional probability, formula for total probability.
Discrete random variables, distributions.
Joint discrete distributions.
Functions of discrete random variables.
Expectation and variance for discrete random variables.
Conditional distributions, conditional expectation.
Continuous random variables, densities, expectation.
Generating and moment generating functions.
Probability 1
2023/2024
Programme:
Financial mathematics, First Cycle
Year:
2 year
Semester:
first
Kind:
mandatory
ECTS:
5
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
Readings
D. Stirzaker, Probability and Random Variables, A beginner's guide, Cambridge University Press, 1999.
G. Grimmett and D. Stirzaker, Probability and Random Processes, Third Edition, Oxford University Press, 1982.
Objectives and competences
Financial mathematics is based on probability theory. This course introduces basic concepts of probability needed for applications.
Intended learning outcomes
Understanding basic concepts of probability and the ability to do calculations with random variables and distributions effectively.
Learning and teaching methods
Lectures, problem sessions.
Assessment
2 midterms or written exam, oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Lecturer's references
BERNIK, Janez, MASTNAK, Mitja, RADJAVI, Heydar. Realizing irreducible semigroups and real algebras of compact operators. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2008, vol. 348, no. 2, str. 692-707. [COBISS-SI-ID 14899289]
BERNIK, Janez, MARCOUX, Laurent W., RADJAVI, Heydar. Spectral conditions and band reducibility of operators. Journal of the London Mathematical Society, ISSN 0024-6107, 2012, vol. 86, no. 1, str. 214-234. [COBISS-SI-ID 16357721]
BERNIK, Janez, MASTNAK, Mitja. Lie algebras acting semitransitively. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2013, vol. 438, iss. 6, str. 2777-2792. [COBISS-SI-ID 16553561]
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, 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, WELLNER, Jon A. An excursion approach to maxima of the Brownian bridge. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 2014, vol. 124, iss. 9, str. 3106-3120. [COBISS-SI-ID 17154393]
