THE RELATIONS BETWEEN MODES OF CONVERGENCE FOR SEQUENCES OF RANDOM VARIABLES

BEXHETI, Bedrije and IBRAIMI, Alit and SADIKI, Flamure and LLESHI POLLOZHANI, Ferzije (2022) THE RELATIONS BETWEEN MODES OF CONVERGENCE FOR SEQUENCES OF RANDOM VARIABLES. Journal of Natural Sciences and Mathematics of UT, 7 (13-14). pp. 90-97. ISSN 2671-3039

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Abstract

In this paper, we are going to analyze the relations between different types of convergence of a random sequence, such as almost sure convergence, convergence in mean square, convergence in distribution and convergence in probability. The convergence in distributions says nothing about the relationship between the random variables X_n and X, while for convergence in probability, the joint distribution of X_n and X is relevant. In the main part of the paper, we are going to prove the theorem which argues that the convergence in probability implies convergence in distribution, and the opposite is not true. But if X_n→c, where c is a constant, then X_n→c, which mean that convergence in probability to a constant is equivalent to convergence in distributions. Also, we give some interesting examples.

Item Type:	Article
Uncontrolled Keywords:	random variable, random sequence, mean square, convergence in distributions
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Unnamed user with email zshi@unite.edu.mk
Date Deposited:	01 Nov 2022 13:04
Last Modified:	01 Nov 2022 13:04
URI:	http://eprints.unite.edu.mk/id/eprint/1126

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