Fundamentals of probability theory

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Fundamentals of probability theory

Code: 255129
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Bojan Basrak
Take exam: Studomat
Load:

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: The goal of the course is to introduce the basics of mathematical analysis in the set of real numbers.

COURSE DESCRIPTION AND SYLLABUS:
1. Introduction: Sigma algebras and rings. Measure and probability.
2. Random variables and their distributions: Distributions of random variables and vectors. Integrals and expectations of random variables. Independence. Borel-Cantelli lemmas and Kolmogorov's law 0-1.
3. Moment and laws of large numbers: Moments, moment inequalities and convergence of random variables. The weak law of large numbers. The strong law of large numbers.
4. Convergence in distribution and coupling: The concept of coupling. Convergence in distribution and in total variation. Chen-Stein method. Convergence towards the Poisson distribution. Convergence towards the Normal distribution. Extensions and applications of central limit theorems. Cramer-Wold device.
5. Additional topics: Applications of probability models. Introduction to the theory of large deviations.
Literature:
1. semester
Mandatory course - Regular study - Financial and Business Mathematics
Consultations schedule: