The Cramer-Rao product of the Fisher information F[rho] and the variance < x(2)> equivalent to integral x(2) rho(x)dx of a probability density rho(x), defined on a domain Omega subset of R-D, is found to have a minimum value reached by the density associated with the ground state of the harmonic oscillator in Omega, when Omega is an unbounded domain. If Omega is bounded, the minimum value of the Fisher information is achieved by the ground state of the quantum box described itself by this domain. (