# random variable

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## ran·dom var·i·a·ble

a variable that may assume a set of values, each with fixed probabilities or probability densities (its distribution), in such a way that the total probability assigned to the distribution is unity; the random variable may be discrete, continuous, or mixed discrete-continuous.
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increases quickly with the number of input random variables M and the degree l of the polynomials; For example, M = 10 and l = 5 lead to L = 3003.
[mu] and [sigma] are the mean and standard deviation of the normal random variable. N is the quadrature order (equal to the number of Gauss point).
Let [X.sub.1] ~ g(x) and [X.sub.2] ~ (1/[kappa])h(x)g(x) be independent random variables. If
Comparing random variables is the essence of the actuarial profession; in order to acquire more general results, we give the notion of weak correlation orders as follows.
The polynomial chaos methods are well suited for the random differential equations, RDE, with a very few number of random variables defining their main coefficients.
For a [member of] (1/3,1/2] and n [member of] N define a random variable [Z.sup.([alpha])].sub.n] : [[0,1].sup.N] [right arrow] R by the formula:
If t [member of] T is fixed, then [X.sub.t] is a random variable, whereas if we fix e [member of] S, [X.sub.e] is a function of time, called a realization or sample path of the process X(t, e).
The assumption of random variables and random disturbance is vital for valid model estimation and testing, and thus this assumption is crucial for macroeconometrics.
where [f.sub.X](X) denotes the joint PDF of the random variables X.
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 .

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