  By 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.
