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===Monte Carlo sampling and Sample Average Approximation (SAA) Method===
A common approach to reduce the scenario set to a manageable size is by using Monte Carlo simulation. Suppose the total number of scenarios is very large or even infinite. Suppose further that we can generate a sample <math>\xi^1,\xi^2,\dots,\xi^N</math> of <math>N</math> replications of the random vector <math>\xi</math>. Usually the sample is assumed to be independent and identically distributed (i.i.d sample). Given a sample, the expectation function <math>q(x)=E[Q(x,\xi)]</math> is approximated by the sample average
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