In the activation market, the Transmission System Operator selects and activates balancing energy bids to cover the system imbalance. Growing use of intermittent energy sources increases uncertainty in system operation and new EU regulations, including a so-called Activation Optimization Function and new Standard Products for manual frequency restoration reserves (mFRR), will change the activation process significantly. However, commonly used price-based bid selection approaches are incapable of taking intertemporal constraints and uncertainty into account in the activation process. This paper presents a new optimization formulation, built on stochastic unit commitment principles, using imbalance forecast scenarios to propose bid activation schedules minimizing expected activation costs. Unlike earlier approaches, intertemporal characteristics of the proposed mFRR product are modeled in detail. The optimization procedure is implemented in a rolling horizon simulation and demonstrated using Norwegian imbalance and market data. Compared to a corresponding deterministic approach, the stochastic strategy significantly reduces activation costs.