Analytic Representation of Probability Density Function of Random Variable in Distributional Sense
Bedrije Bedjeti *
Faculty of Mathematics and Natural Sciences, State University of Tetovo, Tetovo, Republic of North Macedonia.
Mejdin Saliji
Ukshin Hoti University, Prizren, Republic of Kosovo.
Vesna Manova Eraković
Faculty of Mathematics and Natural Sciences, Ss. Cyril and Methodius University, Skopje, Republic of North Macedonia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we have proved that the probability density function \(f(t)\) considered as a distribution has a Cauchy representation in \(O_\alpha^{\prime}\). The distribution space \(O_\alpha^{\prime}\) is intermediate space between \(E^{\prime}\) and \(D^{\prime}\).
Keywords: Space D’, space \(O_\alpha^{\prime}\), Space \(D_{L^b}\), Cauchy representation, random variable, discrete random variable, probability density, analytic representation, support, spectrum