  For distribution regression problem, where a bag of $x$--observations is
mapped to a single $y$ value, a one--step solution is proposed. The problem of
random distribution to random value is transformed to random vector to random
value by taking distribution moments of $x$ observations in a bag as random
vector. Then Radon--Nikodym or least squares theory can be applied, what give
$y(x)$ estimator. The probability distribution of $y$ is also obtained, what
requires solving generalized eigenvalues problem, matrix spectrum (not
depending on $x$) give possible $y$ outcomes and depending on $x$ probabilities
of outcomes can be obtained by projecting the distribution with fixed $x$ value
(delta--function) to corresponding eigenvector. A library providing numerically
stable polynomial basis for these calculations is available, what make the
proposed approach practical.
