The formulation of the above two-stage problem assumes that the second-stage data <math>\xi</math> can beis modeled as a random vector with a '''''known''''' probability distribution (not just uncertain). This would be justified in many situations. For example, <math>\xi</math> could be information derived from historical data and the distribution does not significantly change over the considered period of time. In such situations one may reliably estimate the required probability distribution and the optimization ''on average'' could be justified by the [[law of large numbers]]. Another example is that <math>\xi</math> could be realizations of a simulation model whose outputs are stochastic. The empirical distribution of the sample could be used as an approximation to the true but unknown output distribution.
