In: Statistics and Probability
Suppose you have n suitcases and suitcase i holds Xi dollars where X1, X2, …, Xn are iid continuous uniform (0, m) random variables. (Think of a number like one million for the symbol m.) Unfortunately, you don’t know Xi until you open suitcase i.
Suppose you can open the suitcases one by one, starting with suitcase n and going down to suitcase 1. After opening suitcase i, you can either accept or reject Xi dollars. If you accept suitcase i, the game ends. If you reject, then you get to choose only from the still unopened suitcases.
What should you do? Perhaps it is not so obvious? In fact, you can decide before the game on a policy, a set of rules to follow. We will specify a policy by a vector (t1, … tn) of threshold parameters.