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We extend our results in \cite{hislop_marx_1} on the quantitative continuityproperties, with respect to the single-site probability measure, of the densityof states measure and the integrated density of states for random Schr\"odingeroperators. For lattice models on $\mathbb{Z}^d$, with $d \geq 1$, we treat thecase of non-compactly supported probability measures with finite first moments.For random Schr\"odinger operators on $\mathbb{R}^d$, with $d \geq 1$, we proveresults analogous to those in \cite{hislop_marx_1} for compactly supportedprobability measures. The method of proof makes use of the Combes-Thomasestimate and the Helffer-Sj\"ostrand formula.

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Dependence of the density of states on the probability distribution --  part II: Schr\"odinger operators on $\mathbb{R}^d$ and non-compactly  supported probability measures