Gaussian integrals involving absolute value functions

We provide general formulas to compute the expectations of ab- solute value and sign of Gaussian quadratic forms, i.e. E |� X ,A X� + � b, X� + c| and E sgn(� X ,A X� + � b, X� + c) for centered Gaussian random vector X ,fi xed matrix A, vector b and constant c. Products of Gaussian quadratics are also discussed and followed with several interesting applications.

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