Let X1, . . . , Xn be a collection of iid discrete random variables, and Y1, . . . , Ym a set of noisy observations of such variables. Assume each observation Ya to be a random function of some a random subset of the Xi’s, and consider the conditional distribution of Xi given the observations, namely μi(xi) ≡ P{Xi = xi|Y } (a posteriori probability). We establish a general decoupling principle ...

We consider a simple random walk starting at 0 and leading to 0 after 2n steps. By a generating functions approach we achieve closed formulae for the moments of the random variables `number of visits to the origin' . GENERATING FUNCTIONS ; CATALAN NUMBERS AMS 1991 SUBJECT CLASSIFICATION : PRIMARY 60J15 Let Xk , k = 1, 2, • • • be independent and identically distributed random variables with P{X...

The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y defined by a weighted lattice polynomial of (lattice-valued) random variables is considered in general and in some special cases. The central object of inte...

Visual secret sharing by using generalized random grids is a novel approach for generating nonexpansible shares by artfully utilizing various random variables. Stacking the shares together, secret image can be revealed. This paper proposes a 2 out of 3 visual multiple secret sharing method using generalized random grids. Three secret images (A, B, C) are used for generating three non-expansible...

Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable...

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable.The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest.For this purpose, the concepts o...