On the Simulation of the Mathematical Expectation and Variance of Samples for Gaussian-Distributed Random Variables
Keywords:normal distribution, expectation, variance, random variables, statistical averaging rules
The derivation of propagation rules for the mean and the variance of physical quantities functionally connected by the transformations X2, cosX, √X, and arccosX, which were proposed in Ukr. J. Phys. 61, 345 (2016) and Ukr. J. Phys. 62, 184 (2017), has been analyzed. It is shown that the substantiation of the “error propagation rules” was not based on the fundamentals of probability theory and mathematical statistics. Moreover, the proposed reduction of indices, X → √X and X2 → X, in the roots of the square equations forming a basis for the propagation formulas restricts the values of the normal distribution parameters mX and qX.
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