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We examine how the measure and the number of vertices of the convex hull of arandom sample of $n$ points from an arbitrary probability measure in$\mathbf{R}^d$ relates to the wet part of that measure. This extends classicalresults for the uniform distribution from a convex set [B\'ar\'any and Larman1988]. The lower bound of B\'ar\'any and Larman continues to hold in thegeneral setting, but the upper bound must be relaxed by a factor of $\log n$.We show by an example that this is tight.

Random polytopes and the wet part for arbitrary probability distributions