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- W145280227 abstract "1. Motivation of the problem. Let AI, A2, ..., A n be events in the sense of probability theory and let B r denote the event that exactly r of the A's occur. A frequent problem is to evaluate the probability P(Br) of B r in terms of the probabilities of products of the A's. As an example, consider the following problem. Let Y. 3 be the amount an insurance company has to pay out on the j-th day of the year. Evidently, Yj varies from day to day and the company should be able to pay the largest claim, but it is a loss in financial terms if a much larger amount is kept in the bank account of the company than needed for the operations. That is, the company is in= max(Y 1 Yn ) . = terested in the behaviour of Z n .... , . Let A 3 {Yj ~ X], where x is a given number. Then B 0 = {none of the Aj's occursl = [Yj < x for all j] = {Z n < x]. A similar situation arises if Y. denotes the time needed for servicing the j-th component of a 3 = {Yj machine, where j = i, 2 ..... n. Again, if Aj ~ x}, then B 0 = [Z n < x}. Evidently, Z n is the time needed for the completion of the service of the machine, if servicing starts on all components at the same time. In both cases, B 1 describes the behaviour of the second largest among the Y's, and in general, B r is related to the (r + l)-st largest of the Y's. Usually values of" @default.
- W145280227 created "2016-06-24" @default.
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- W145280227 date "1972-01-01" @default.
- W145280227 modified "2023-09-25" @default.
- W145280227 title "The role of graph theory in some sieve arguments of probability theory" @default.
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- W145280227 doi "https://doi.org/10.1007/bfb0067360" @default.
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