Introduction. The mathematical theory of probability is now ordinarily formulated in terms of measure theory. The formalization of a succession of n trials is in terms of ^-dimensional measure ; that of a sequence of trials is in terms of (denumerably) infinite-dimensional measure ; that of a continuous set of trials (a set dependent on a continuous time parameter say) is in terms of measure in...

We report experimental results on the acceleration component probability distribution function at R λ = 690 to probabilities of less than 10 −7. This is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55. We compare our probability distribution to those predicted by several mode...

Suppose that in the four tests Alice’s scores are 90, 95, 85, 90, and Bob’s scores are 85, 95, 90, 90. How to evaluate their scores? In this paper, we introduce the concept of ordered probability mass function which can be used to find a probability mass function with smaller variance. More interestingly, we can use it to distinguish sequences of positive numbers statistically.

In this paper, the residual probability function is applied to analyze survival of two used components relative each other in case when their lifetimes are dependent. The expression by copulas has been derived along with some examples particular copulas. behaviour terms underlying dependence also discussed. order considered dependent case. class Archimedean copulas, we prove that implies usual ...

we describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. we present a new method for computing, electronic transport wave function and greens function of the disordered graphene. in this method, based on the small rectangular approximation, break up the potential barriers in to small parts. then using the f...