On One Problem of the Optimal Choice of Record Values

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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.