Electronic and phonon band structure, thermodynamic and optical properties are studied for the CdTe crystal. We calculated the electron and phonon dispersion at high symmetry directions, density of electron and phonon state, temperature dependence feature of Raman spectra, heat capacity, free energy, entropy, enthalpy and Debay temperature estimated with the generalized gradient approximation (GGA). A Perdew–Burke–Ernzerhof functional (PBE) was utilized. To study the optical properties was use a complex dielectric function ε(ħω). All of the calculated parameters correlate well with the known experimental data.

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This paper presents theoretical studies of formation regularities for the statistical mean and variance of normally distributed random values with the unlimited argument values subjected to nonlinear transformations of functions $\sqrt{|X|}$ and $\sqrt{X}$. It is shown that for nonlinear square root transformation of a normally distributed random variable, the integrals of higher order mean $n>1$ satisfy the inequality $\overline{(y-\overline{Y})^n}\neq 0$. On the basis of the theoretical research, the correct boundaries $m,\sigma \to \infty$ of error transfer formulas are suggested.