This paper generalizes certain analytical formulas for yield and yield sensitivities so that design centering and yield optimization can be effectively carried out employing given statistical parameter distributions. The tolerance region of possible outcomes is discretized into a set of orthotopic cells. A suitable weight is assigned to each cell in conjunction with an assumed uniform distribution on the cell. Explicit formulas for yield and its sensitivities w.r.t. nominal parameter values and component tolerances are presented for linear cuts and sensitivities of these cuts based upon approximations of the boundary of the constraint region. To avoid unnecessary evaluations of circuit responses, e.g., integrations for nonlinear circuits, multidimensional quadratic interpolation is performed. Sparsity is exploited in the determination of these quadratic models leading to reduced computation as well as increased accuracy.