Before revision:  Both types of data points are i.i.d. draws from an unknown distribution . We consider the two canonical objectives for online selection---maximizing the probability of selecting the maximum and maximizing the expected value of the selection---and provide the first performance guarantees for both these objectives in the streaming model .
After revision:  Both types of data points are i.i.d. random variables whose distribution is itself drawn, according to a known distribution, from a finite set of known candidate distributions. This implies a tight prophet inequality for exchangeable sequences of random variables, answering a question of Hill and Kertz (Contemporary Mathematics, 1992), but leaves open the possibility of better guarantees when the number of candidate distributions is small, a setting we believe is of strong interest to applications .