2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119991By the example of a Fourier transform, the possibilities of Hilbert space geometry applications for statistical model construction are analyzed. In accordance with Bohr's complementarity principle, mutually-complementary coordinate and momentum representations are presented. It was demonstrated that the characteristic function of coordinate distribution may be considered as a convolution of the psi-function in momentum representation and vice versa. The naturalness of coordinate and momentum operators introduction is demonstrated. A probabilistic interpretation of Hilbert space geometry is given. Cauchy-Bunyakowsky (Cauchy-Schwartz), Cramer-Rao and uncertainty inequalities are considered in the same framework. The principal postulates of quantum informatics as a natural science are presented. It is demonstrated that quantum informatics serves as a theoretic basis for both probability theory and quantum mechanics.22 pagesQuantum PhysicsData Analysis, Statistics and Probabilitytext