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As we replace conventional synchronous generators with renewable energy, the frequency security of power systems is at higher risk. This calls for a more careful consideration of unit commitment (UC) and primary frequency response (PFR) reserves. This paper studies frequency-secured UC under significant wind power uncertainty. We coordinate the thermal units and wind farms to provide frequency support, wherein we optimize the variable inverter droop factors of the wind farms for higher economy. In addition, we adopt distributionally robust chance constraints (DRCCs) to handle the wind power uncertainty. To depict the frequency dynamics, we incorporate a differential-algebraic equation (DAE) with the dead band into the UC model. Notably, we apply Bernstein polynomials to derive tight inner approximation of the DAE and obtain mixed-integer linear constraints, which can be computed in off-the-shelf solvers. Case studies demonstrate the tightness and effectiveness of the proposed method in guaranteeing frequency security.