Abstract
A random sample J1J2, ..., Jn is drawn from a population of size N≦n Suppose there is a reward which depends only on the value of JT, where T is any stopping time. Then there is a stopping rule for the case of sampling without replacement which yields a higher expected reward than that yielded by any stopping rule for the case of sampling with replacement. The same is true if the reward depends on T and JT, provided some monotonicity restrictions are satisfied.
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