Consider a news vendor problem as in Section 1.1. Suppose this problem is solved using a sampling approach. The sampled problem with continuous cumulative distribution function Fν has a solution a  ....

Consider a news vendor problem as in Section 1.1. Suppose this problem is solved using a sampling approach. The sampled problem with continuous cumulative distribution function Fν has a solution a
 . Find the distribution of this quantile and show how to construct a confidence interval around x .

Q24:

Consider Example 1. First, verify the assumptions in Theorem 7. Solve 100 samples each for ν = 10 + 10i for i = 0,1,...,10 . Use these observations to estimate values for α and β in Theorem 7 for ε = 0.03

Theorem 7.

Suppose the two-stage stochastic program in (1.1) is feasible and has simple recourse and that ξ has finite second moments. Then Q(x) is finite if and only if q+ i +q− i ≥ 0 with probability one.