This example deals with 48 uncertain parameters, which are considered as uniform

random variables having an uncertainty of 20% around their nominal values given in Fig.

Probabilistic load flow, which incorporates dependence between

random variables, is an efficient tool in probabilistic analysis as it enables a comprehensive assessment of system working conditions, thus could inform system operators of the weak points and potential crisis under various uncertainties [5].

From Theorem 1, the extended Birnbaum-Saunders distribution has density (9) and from Theorem 3 we can generate

random variables X ~ EBS([alpha], [beta], [xi]).

Denuit, "Comonotonicity, orthant convex order and sums of

random variables," Statistics & Probability Letters, vol.

Based on the superposition principle, the random differential equation with an input depending on several

random variables is decomposed on a sequence of RDE with the same main random operator and reduced right-hand sides.

Let [([F.sub.n]).sub.n[member of]N] be a filtration and [([X.sub.n]).sub.n[member of]N] be a sequence of

random variables. We say that [([X.sub.n]).sub.n[member of]N] is a martingale adapted to the filtration [([F.sub.n]).sub.n[member of]N] if for every n [member of] N

Since the states (the values of the

random variable [X.sub.k]) are the same for each k, one only needs the second row to describe the pdf.

Apparently, Haavelmo was simply 'considering' that economic variables are

random variables because he needed this assumption.

In structural reliability problem, let us assume that the limit-state function is g(x, y) = g([x.sub.1], [x.sub.2], ..., [x.sub.n], [y.sub.1], [y.sub.2], ..., [y.sub.m]), where x = ([x.sub.1], [x.sub.2], ..., [x.sub.n]) is a n-dimensional vector of

random variables and y = ([y.sub.1], [y.sub.2], ..., [y.sub.m]) is a m- dimensional vector of interval variables.

Figure 2 demonstrates how the hyperplane (line), which is the line of a constant sum of the values of the

random variables and is perpendicular to the n-cube's (square's) main diagonal, accrues volume (area) below it.