High penetration of wind generation will increase the requirement for fast frequency response services as currently wind plants do not provide inertial response. Although the importance of inertia reduction has been widely recognized, its impact on the system scheduling has not been fully investigated. In this context, this paper proposes a novel mixed integer linear programming (MILP) formulation for stochastic unit commitment that optimizes system operation by simultaneously scheduling energy production, standing/spinning reserves and inertia-dependent fast frequency response in light of uncertainties associated with wind production and generation outages. Post-fault dynamic frequency requirements, rate of change of frequency, frequency nadir and quasi-steady-state frequency are formulated as MILP constraints by using the simplified model of system dynamics. Moreover the proposed methodology enables the impact of wind uncertainty on system inertia to be considered. Case studies are carried out on the 2030 Great Britain system to demonstrate the importance of incorporating inertia-dependent fast frequency response in the stochastic scheduling and to indicate the potential for the proposed model to inform reviews of grid codes associated with fast frequency response and future development of inertia-related market.