This paper considers an extension of probability space based on interval random variables. In this approach, first, a notion of interval random variable is introduced. Then, based on a family of continuous distribution functions with interval parameters, a concept of probability space of an interval random variable is proposed. Then, the mean and variance of an interval random variable are intr...

In this paper, we obtain some Rosenthal’s type inequalities for negatively orthant dependent (NOD) random variables.

Let be a stationary sequence of pair wise negative quadrant dependent random variables with survival function {,1}nXn?F(x)=P[X>x]. The empirical survival function ()nFx based on 12,,...,nXXX is proposed as an estimator for ()nFx. Strong consistency and point wise as well as uniform of ()nFx are discussed

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.