The best choice problem with an unknown number of objects

The secretary problem with a known prior distribution of the number of candidates is considered. If ,, where and , is the prior distribution of the number N of candidates it will be shown that, if the optimal stopping rule is of the simple form, then the optimal stopping index satisfies asymptotically the equation . The probability of selecting the best object by the corresponding policy will be . The paper also gives an example of the distribution p for which the optimal stopping rule consists of a stopping set with two islands. It presents an asymptotical solution for this example.