# Normal random variable

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## Normal Random Variable

A random variable on a chart that is distributed at some point along a bell curve. See also: Normal probability distribution.
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For normal random variables, X can be transformed into standard normal random variables u through a linear transformation, as follows:
A normal or non-normal random variable Z can be approximated using one-dimensional Hermite orthogonal polynomials [[PSI].sub.i] of the standard normal random variables [xi] as [17,18]
where [[alpha].sub.j] = [m.sub.j]/(1 + [b.sup.2.sub.j]), [[beta].sup.2.sub.j] = 2[[psi].sup.-1.sub.j] - 1 + 2[square root of [[psi].sup.-1.sub.j]] [square root of 2[[psi].sup.-1.sub.j] - 1], and [Z.sub.Vj] are independent standard normal random variables.
The reflectivity is generated as [b.sup.3] (n), where b(n) are independent normal random variables with zero mean and variance 0.28.
In order to measure the (in)efficiency of Parliament in Asian countries, in this paper we propose a stochastic frontier production function for unbalanced panel data  assumed to be distributed as a half normal random variables. This type of frontier and the computation method present advantages with respect other alternatives, for example the deterministic frontiers [12,16].
zero-mean normal random variables x , y , and z with standard deviation [[sigma].sub.xyz] so that the new position of the receiver is now at coordinates (D + x',y',z').
For all scenarios, we assume that the bivariate normal random variables (X, Y) have population parameters [[mu].sub.x] = 0, [[sigma].sub.x.sup.2] = [[sigma].sub.y.sup.2] = 1.
are normal random variables with mean zero and covariance structure :
To view this issue from a different perspective, a chi-squared random variable with n degrees of freedom arises from summing the squares of n independent normal random variables. Hence, a chi-squared random variable with 1 degree of freedom is simply the square of a normal random variable.
where Z = [([Z.sub.1], ..., [Z.sub.m]).sup.T] is a random vector consisting of m mutually independent standard Normal random variables, A is an n x m matrix, [mu] is an n x 1 vector and [??] stands for "equality in distribution." The relationship between [SIGMA] and A is given by [SIGMA] = [AA.sup.T].
Moreover, if the relative price changes in each holding period are independently and identically distributed normal random variables, the empirical volatilities, [S.sub.23], are related to the chi-square random variable [[chi].sub.k.sup.2] = by [[chi].sub.k.sup.2] = k h [S.sub.23.sup.2] where k = n -1 and n is the number of trading days in the holding period, in this case 23.
randn for normal random variables, and rand for continuous uniform
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