Clearly, for any [alpha] [member of] (1/3,1/2] and any natural numbers i [not equal to] j the

random variables [Z.sup.([alpha])].sub.n] and [Z.sup.([alpha])].sub.j] are independent.

random variables satisfying (5) and (9), and {[X.sub.i], i [greater than or equal to] 1} be a sequence of arbitrary

random variables and independent of [sigma]'s.

They are based on computer simulations involving random number generators and are used to make predictions about processes involving

random variables. A computer code that replicates a certain phenomenon can be put in a loop, be simulated any number of times and, based on the outcomes, conclusions about its real life behaviour can then be drawn.

The Saddlepoint Approximations (SPA) is an accurate statistical method to efficiently estimate the PDF and CDF of a function Y = g(Z) of

random variables Z = [[Z.sub.1], [Z.sub.2],...

The condition ([e.sub.2] - [e.sub.1]) [p.sub.2] [less than or equal to] (w - [p.sub.1] * L - [e.sub.1])-(w - [p.sub.2] * L - [e.sub.2]) for [e.sub.2] > [e.sub.1] implies that lower levels of self-protection yield larger

random variables in the increasing convex order.

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

random variables because he needed this assumption.

Moreover, we can suggest that a source of difficulties for solving the structural reliability problem by any method is its dimensionality, determined by the number of

random variables n [41].

Since round-off errors for

random variables that are rounded to the nearest integer are distributed Uniform (-1/2, 1/2), the sum of round-off errors is a linearly transformed Irwin-Hall distribution [12].

Assume initial values for the design point in the real space [X.sup.*] = [([X.sub.1], ..., [X.sub.n]).sup.T] and evaluate the corresponding values for the limit state function g(X) (e.g., assume an initial design point as the mean values of

random variables).

The interaction of

random variables with gene expression data alone provides a marginal improvement in the fit; however, when two or more

random variables interact, the lack of information in each variable translates into poorer fit of the linear model to the radiation sensitivity outcome.

In this paper, variation coefficients of

random variables were introduced to estimate dispersion of sample points, and so that mean and standard deviation are both taken into account.

In practice, families of orthonormal polynomials are associated in terms of probability distributions of input

random variables.