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are widely used, while developing models to describe, e.g., the elastically deformed state of a static body by the potential energy method, a moving body by the kinetic energy method, electric heaters by the Joule heat generation method, and so forth. If the corresponding input parameters undergo random fluctuations, then, in most cases, a statistical model of physical regularity can be constructed by studying the nonlinearly transformed quantity. Similar problems are challenging, e.g., in optics and quantum mechanics,

Analytical Relations for the Mathematical Expectation and Variance of a Standard Distributed Random Variable Subjected to the √X Transformation