On One Problem of the Optimal Choice of Record Values
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Independent random variables X1, X2, . . . , Xn having U([0, 1])-uniform distribution and upper record values in this set are considered. We study the problem of maximizing (taking into account some consecutively observed values x1, x2, . . . , xk of these X’s) the expectation of sums of records in this sequence under the optimal choice of the corresponding variable Xk (instead of X1) as the initial record value.
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