A two-stage stochastic programming approach is pursued to optimally place and size photovoltaic (PV) inverters in a radial distribution network under solar irradiance and load uncertainties. First-stage variables include binary PV unit placement as well as continuous real and apparent power capacities of the inverters. Second-stage decisions comprise reactive power compensation, power flows, and nodal voltages, which are determined adaptively to the uncertainty. The objective is to minimize installation cost and expected thermal losses on the network. The optimization problem is formulated as a mixed-integer second-order cone program and is tested on a practical distribution network.