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

  • P. Kosobutsky National University “Lviv Polytechnic”
Keywords: normal distribution, mathematical expectation, variance, random variables, direct quadratic transformation, inverse quadratic transformation, errors

Abstract

The mathematical expectation and the variance have been calculated for random physical variables with the standard distribution function that are transformed by functionally related direct quadratic, X2, and inverse quadratic, √X, dependences.

References


  1. G.G. Rode. Propagation of measurement errors and measured means of a physical quantity for the elementary functions cos x and arccos x. Ukr. J. Phys. 61, 345 (2016).
    https://doi.org/10.15407/ujpe61.04.0345

  2. G.G. Rode. Propagation of measurement errors and measured means of a physical quantity for the elementary functions x2 and vx. Ukr. J. Phys. 62, 184 (2017).
    https://doi.org/10.15407/ujpe62.02.0184

  3. A. Hald. Statistical Theory with Engineering Applications (Wiley, 1952).

  4. J.K. Patel, C.B. Read. Handbook of the Normal Distribution (M. Dekker, 1982).

  5. A. Papoulis. Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

  6. L. de Broglie. Heisenberg's Uncertainties and the Probabilistic Interpretation of Wave Mechanics: With Critical Notes of the Author (Springer, 1990).
    https://doi.org/10.1007/978-94-009-2127-6

  7. H. Dwight. Tables of Integrals and other Mathematical Data (Macmillan, 1961).

  8. I.S. Gradshtein, I. M. Ryzhik. Table of Integrals, Series, and Products (Academic, 1980).
Published
2018-04-20
How to Cite
Kosobutsky, P. (2018). Analytical Relations for the Mathematical Expectation and Variance of a Standard Distributed Random Variable Subjected to the √X Transformation. Ukrainian Journal of Physics, 63(3), 215. https://doi.org/10.15407/ujpe63.3.215
Section
General physics