Heating, Ventilation and Air Conditioning (HVAC) systems play a fundamental role in maintaining acceptable thermal comfort and Indoor Air Quality (IAQ) levels, essentials for occupants well-being. Since performing this task implies high energy requirements, there is a need for improving the energetic efficiency of existing buildings. A possible solution is to develop effective control strategies for HVAC systems, but this is complicated by the inherent uncertainty of the to-be-controlled system. To cope with this problem, we design a stochastic Model Predictive Control (MPC) strategy that dynamically learns the statistics of the building occupancy and weather conditions and uses them to build probabilistic constraints on the indoor temperature and CO2 concentration levels. More specifically, we propose a randomization technique that finds suboptimal solutions to the generally non-convex stochastic MPC problem. The main advantage of this method is the absence of apriori assumptions on the distributions of the uncertain variables, and that it can be applied to any type of building. We investigate the proposed approach by means of numerical simulations and real tests on a student laboratory, and show its practical effectiveness and computational tractability.