We prove the Hölder-continuity of the density of states measure (DOSm) and the integrated density of states (IDS) for discrete random Schrödinger operators with finite-range potentials with respect to the probability measure. In particular, our result implies that the DOSm and the IDS for smooth approximations of the Bernoulli distribution converge to the corresponding quantities for the Bernoulli-Anderson model. Other applications of the technique are given to the dependency of the DOSm and IDS on the disorder, and the continuity of the Lyapunov exponent in the weak-disorder regime for dimension one. The talk is based on joint work with Peter Hislop (Univ. of Kentucky)