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 ...

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...

in this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. the results on i.i.d case of soo hak sung [9] are generalized and extended.