To the best of our knowledge this is the first attempt to formulate a statistical optimization problem for process variation aware design by Integer Linear Programming. We formulate task scheduling and mapping for a typical MPSoC platform in order to maximize the Energy Yield of the system while meeting the timing constraint of the system. Energy Yield is defined as the probability that the MPSoC instance meets the energy constraint of the system. Moreover, we show how our statistical optimization algorithm results in better energy yield over the deterministic approach, which tries to optimize only the worst-case energy consumption of the system under process variation.