The formulation of the above two-stage problem assumes that the second-stage data <math>\xi</math> is modeled as a random vector with a '''''known''''' probability distribution. This would be justified in many situations. For example, the distribution of <math>\xi</math> could be information derivedinferred from historical data andif one assumes that the distribution does not significantly change over the considered period of time. In such situations one may reliably estimateAlso, the required probabilityempirical distribution andof the optimization ''on average''sample could be justifiedused byas an approximation to the [[lawdistribution of largethe numbers]].future Anothervalues example is thatof <math>\xi</math>. couldIf beone realizations ofhas a simulationprior model whosefor outputs<math>\xi<math>, are stochastic. The empirical distribution of the sampleone could beobtain useda asposteriori andistribution approximationby toa theBayesian true but unknown output distributionupdate.
