t](e) is a discrete

random variable for all t [member of] T and continuous-state if [X.

As mentioned, the original composite limit state method is exact for problems with linear instantaneous limit state functions of at most two

random variables.

According to the distribution state and related calculation formula of the above three

random variables, the experimental result comparisons of

random variables under different sample size m and same sample size by MC method and QMC method can be seen in table 2 and table 3.

The nth moment of the

random variable X given by (3) can be obtained using the formula

Because the irrelevance and the independence are equivalent for Gaussian

random variables, [s.

All these problems stem from a very special property of the geometric mean: a positive

random variable may have a geometric mean of 0.

In the present paper, we show an exponential inequality for the negatively associated

random variables which improves some known results, such as, Kim and Kim [10], Sung [25, 26], Xing et al.

In this way we can easily also obtain PDF of

random variable d, as [f.

Since linear transformation applied to Gaussian

Random variables does not change its property [6], so we introduce such type of transformation as, Y = (X mx)/sx in order to convert this PDF into standard Gaussian PDF [7], whose mean is zero and variance equal to unity.

A

random variable X is said to have an extended beta (type 1) distribution with parameters [alpha], [beta] and [lambda], denoted by X ~ EB1([alpha], [beta]; [lambda]), if its pdf is given by (Chaudhry et al.

notation of Example 1, let a be a

random variable with the complex

Let L be a

random variable denoting the number of correctly placed objects.