Konvergencija nizova slučajnih varijabli

In this paper we deal with a part of probability theory related to the convergence of sequences of random variables. There is four types of convergence, and they are: convergence in distribution, convergence in probability, convergence in mean and almost sure convergence. Each type of convergence is explained in detail and for each type the accompanying theorems and propositions necessary for determining convergence are attached. Also, everything is accompanied by illustrative examples or some practical applications. Some of these applications are important results in probability theory, such as: weak law of large numbers, strong law of large numbers, central limit theorem, etc. Emphasis is also placed on the relationships between individual types of convergence and on the convergence of the transformed continuous random variable. Finally, it is important to note that each type of convergence is generalized on the example of a random vector.