The authors consider the practical determination of an optimal control random system in which both the dynamics and the cost function involve a random parameter defined by its probability space. This is basically an applied paper and the purpose is to develop a computational framework as well as necessary conditions for validation and verification of the solutions. The key of the approch is that in order to achieve these objectives, one follows a statistical technique based on a sample average scheme: the cost function is replaced by the mean value of a sample. The authors introduce the uncertainty control problem, define the averaging approximate optimal control problem, derive optimality conditions for the approximate problem, and then they check the consistency of the approximation. They conclude the paper with some numerical examples.