Abstract
We consider probability functions of parameter-dependent random inequality systems under Gaussian distribution. As a main result, we provide an upper estimate for the Clarke subdifferential of such probability functions without imposing compactness conditions. A constraint qualification ensuring continuous differentiability is formulated. Explicit formulae are derived from the general result in the case of linear random inequality systems. In the case of a constant coefficient matrix, an upper estimate for even the smaller Mordukhovich subdifferential is proven.
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