Applications of Dirac delta generalized function to theory of distributions of random variables

ABSTRACT Master of Science Thesis APPLICATIONS OF DIRAC DELTA GENERALIZED FUNCTION TO THEORY OF DISTRIBUTIONS OF RANDOM VARIABLES YELİZ MERT Anadolu University Graduate School of Natural and Applied Sciences Statistics Program Supervisor: Prof. Dr. Embiya A?AO?LU 2003, 75 pages In this thesis, a method of obtaining distributions of transformed random variables was developed. This method based on the Heaviside generalized function, the Dirac delta generalized function and can be considered as alternative to classical Change of Variable and Distribution Functions methods. Mentioned method allowed to obtain the distribution functions or the density functions of continuous random variables, and also defined the concept of generalized density function for discrete random variables. So, the opportunity of examining continuous random variables and discrete random variables in the same way was obtained. Keywords : Heaviside generalized function, Dirac delta generalized function, Generalized function ii