Asymptotic theory of selection by relative rank with medium cost

Selection from among n objects by relative rank with no recall - the ‘secretary problem’ - in the asymptotic case when was considered, assuming that k, the cost ratio, is a finite constant. The essential part is what shall be called Phase 1, where the number of observations i remains to be . Then the expected number of observations is of course . The expected value of the attained absolute rank is also . It is interesting to note that, with the optimal rule, the expected cost of observations comes out to be equal to the expected rank.