  We consider discrete Schr\"odinger operators on $\ell^2(\mathbb{Z})$ with
bounded random but not necessarily identically distributed values of the
potential. We prove spectral localization (with exponentially decaying
eigenfunctions) as well as dynamical localization for this model. An important
ingredient of the proof is a non-stationary version of the parametric
Furstenberg Theorem on random matrix products, which is also of independent
interest.
