Technical Note - Statistical Measures for Linear Functions on Polytopes

This note presents a technique for obtaining a random sample from an arbitrary N-dimensional bounded convex polyhedral set (polytope). The need for computing the expected value and variance measures for linear functions defined on such sets arises in multiattribute decision problems and in certain classes of linear programming problems. We develop the method and produce formulations for estimating the statistical measures for linear functions. A simple example is presented.