  Pencils of Hankel matrices whose elements have a joint Gaussian distribution
with nonzero mean and not identical covariance are considered. An approximation
to the distribution of the squared modulus of their determinant is computed
which allows to get a closed form approximation of the condensed density of the
generalized eigenvalues of the pencils. Implications of this result for solving
several moments problems are discussed and some numerical examples are
provided.
