The inverse moment problem deals with the reconstruction of a probability density function (PDF) of a random variable (RV) by means of its statistical moments. In the special case of the Hausdorff moment problem, where the PDF has a finite support, how could one estimate this support using the moments?
Note that, without loss of generality, the Hausdorff moment problem is usually solved for the standard support of $[0,1]$. But we must know what is the support of our PDF before transforming the RV to the mentioned standard support.
A related paper: http://www.sciencedirect.com/science/article/pii/S0167715208000539