Question

this question is from the book Probability and Stochastic Processes (3rd Edition) by Yates question 5.10.10

2. Problem 5.10.10 Suppose you have n suitcases and suitcase i holds I dollars where Xi. X. I are iid continuous uniform (0. m) random variables. Think of mber ke one milion for the symbo m.) Unfortunately, you don t know X, until you open suitcase 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 X dollars. If you accept suitcase i, the game ends. If you reject, then you get to choose only from the stil1 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 wll specify a policy by a vector (n. . t) of threshold parameters After opening suitcase i. you accept the amount X, if Otherwise, you reject suitcase i and open suitcase i-1. If you have rejected suitcases n down through 2, then you must accept the amount Xin suitcase 1. Thus the threshold 0 since you never reject the amount in the last suitcase. If you have rejected suitcases n down through 2, then you must accept the amount X in suitcase1. Thus the threshold η:0 since you never reject the amount in the last suitcase (a) Suppose you reject suitcase through i, but then you (b Let Wk denote your reward given that there are k unopened (c) As a function of find a recursive relationship for E[1%) d) For FA suitcases, find the policy (T. .. T) that accept suitcase i. Find E[X,LP「ij, suitcases remaining. What is A 1? in terms of and EtkJ. maximizes

Answer 1

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