Fuzzy statistics and random variables represent a progressive fusion of traditional probability theory with the principles of fuzzy logic, enabling the treatment of imprecision and vagueness inherent ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

- Because we made a coding mistake. - Because the average of the x is random. - **Because the average of the samples is a random variable.** - All of the above. We are now going to increase the number ...

Extropy has emerged as a pivotal measure in the quantification of uncertainty, serving as a complementary counterpart to the traditional concept of entropy. Unlike entropy, which is widely used to ...

The purpose of this project is to familiarize students with the realization of probabilistic methods with simulations and coding. The first question introduces the idea of calculating expected value ...

ABSTRACT: This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a ...

ABSTRACT: In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We ...