Sheldon M. Ross

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A typical approach to estimate an unknown quantity is to design an experiment that produces a random variable Z distributed in 0; 1] with EZ] = , run this experiment independently a number of times and use the average of the outcomes as the estimate. In this paper, we consider the case when no a priori information about Z is known except that is distributed(More)
We provide sufficient conditions for the following types of random variable to have the increasing-failure-rate (IFR) property: sums of a random number of random variables; the time at which a Markov chain crosses a random threshold; the time until a random number of events have occurred in an inhomogeneous Poisson process; and the number of events of a(More)
A typical approach t o estimate an unknown quantity p is t o design an experiment that produces a random variable Z distributed in [0,1] with E[Z] = p, run this experiment independently a number of times and use the average of the outcomes as the estimate. In this paper, we consider the case when no a priori information about Z is known except that is(More)
We are told that an object is hidden in one of m(m < ») boxes and we are given prior probabilities p. that the object is In the i box. A search of box i costs c. and finds the object with probability a. if the object is in the box. Also, we suppose that a reward R. is earned if the object Is found in the i box. A strategy is any rule for determining when to(More)
The coupon subset collection problem is a generalization of the classical coupon collecting problem, in that rather than collecting individual coupons we obtain, at each time point, a random subset of coupons. The problem of interest is to determine the expected number of subsets needed until each coupon is contained in at least one of these subsets. We(More)