In mobile networks, traffic fluctuates heavily over time which rises uncertainty in the cell load for an eNodeB. Conventional radio network planning (RNP) focuses on a static model for the traffic distribution which is usually taken at hours of peak demand. However, a major disadvantage of such a deterministic model is that the locations of the eNodeBs are not optimized for the various traffic distributions that vary across the day which decreases the average network's throughput or the end user's QoS at off-peak hours. The main contributions of this work are the following. First, we present a stochastic approach for LTE RNP that optimizes the eNodeBs locations taking into account various traffic distributions or the uncertainty of the traffic distribution over time. Second, we formulate the LTE RNP under uncertainty as a stochastic optimization problem that is solved to optimality for multiple scenarios. Finally, we apply a dynamic eNodeB switching on/off strategy to reduce the energy consumption. Simulation results show that significant increase in the network throughput can be achieved, if RNP is done taking into account the uncertainty of the traffic distribution compared to a deterministic traffic model. Moreover, switching off eNodeBs during low traffic states leads to a more energy efficient wireless network operation.