Statistical Analysis of Normally Distributed Data with a Limited Scattering Interval of Values Converted by Direct g(x) = x2; cos x; ax and Inverse Functions
Keywords:normal distribution, mathematical expectation, variance, random variables, calculation and transfer of errors, transformation of a random variable with elementary functions
The work is devoted to the theoretical analysis of the correct application of the model of a continuous normally distributed random variable in the substantiation of the so-called error transfer formulas in the problem of a statistical processing of experimental data. Attention is paid to the role of limiting the scattering interval of values of a random variable subjected to nonlinear direct g(X) transformation by elementary functions X2; aX and cos X, as well as the inverse g-1(X) = √X, arccos X, loga X to them. The regularities of the statistical averaging of the data obtained by the disorder of the Taylor transform functions are studied. To confirm the validity of the obtained results, the method of quadratic functional optimization is used.
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