We consider a sequential rule, where an item is chosen into the group, such as a university faculty member, only if his score is better than the average score of those already belonging to the group. We study four variables: The average score of the members of the group after k items have been...

Let X_n,…,X₁ be i.i.d. random variables with distribution function F and finite expectation. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X's using stopping rules. The statistician's goal is to select a value of X as large as possible. Let V_n²...

A new Secretary Problem is considered, where for fixed k and m one wins if at some time i = m(j .. 1) + 1 up to jm one selects one of the j best items among the first jm items, j = 1,...,k. Selection is based on relative ranks only. Interest lies in small k values, such as k = 2 or 3. This is...

The classical Bomber problem concerns properties of the optimal allocation policy of arsenal for an airplane equipped with a given number, n, of anti-aircraft missiles, at a distance t 0 from its destination, which is intercepted by enemy planes appearing according to a homogeneous Poisson...

The classical secretary problem for selecting the best item is studied when the actual values of the items are observed with noise. One of the main appeals of the secretary problem is that the optimal strategy is able to find the best observation with the nontrivial probability of about 0.37,...

The secretary problem for selecting one item so as to minimize its expected rank, based on observing the relative ranks only, is revisited. A simple suboptimal rule, which performs almost as well as the optimal rule, is given. The rule stops with the smallest i such that Ri = ic/(n + 1 - i) for...

A problem of optimally allocating partially effective ammunition x to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time t, known as the Bomber Problem, was first posed by Klinger and Brown (1968). They conjectured a set of apparently...

The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, F, belongs to the Gumbel domain of attraction of extreme value distribution. This class contains the Normal, log Normal, Gamma,...

A version of a secretary problem is considered: Let X_j, j = 1,...,n be i.i.d. random variables. Like in the classical secretary problem the optimal stopper only observes Y_j = 1, if X_j is a (relative) record, and Y_j = 0, otherwise. The actual X_j-values are not revealed. The goal is to maximize...

Let X_i be nonnegative independent random variables with finite expectations and X^*_n = max {X_1, ..., X_n}. The value EX^*_n is what can be obtained by a ``prophet". A ``mortal" on the other hand, may use k = 1 stopping rules t_1, ..., t_k yielding a return E[max_{i=1, ..., k} X_{t_i}]. For n...