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A difficult open problem is whether also the GGC-class is closed with respect to multiplication of independent random variables.
2])" notation for random variable with normal distribution in the interval (-[infinity, [infinity]]).
We would like to point out that the random variables [X.
The resistance term for the strength limit state is a normalized random variable corresponding to the actual value, taken from the IGTP (Green and Evans 1987) for the given species/size/grade (mapped as needed), divided by the nominal value from the era being considered.
are all independent random variables with the same distribution (so they have a common expectation E(X)), and if the random variable N is independent of all the X's, then "Addition Law for the Expectation of a Random Sum" states:
All random variables (R, P, Y, and A) are observed for the same time period; therefore, subscripts are not shown here or in other equations.
Let X be a unimodal random variable with support [a, b] and variance [[sigma].
With an adequate number of samples from each layer, the expected value and the type of distribution for the random variable of the modulus E can be estimated.
n] is a sequence of random variables such that for every [member of] > 0,
For a given probability level p [member of] (0, 1), we denote the VaR or quantile of the loss random variable X by [F.
which is the characteristic function of a random variable with distribution function
where the probability is taken over random variable R which is uniformly distributed over [{0,1}.