Predrag M. Rajkovic, Sladjana D. Marinkovic, Miomir S. Stankovic
Published 2013-04-08Version 1
We consider the linear combinations of elements of two sequences: the first one a priory given nonnegative sequence and the second random sequence from the unit interval. We investigate the expected value of the smallest natural number such that the value of these linear combinations exceed a positive number. After very clear geometrical conclusions, we find the function which expresses the expected value. Here, we recognize a few known results like the special cases.
Comments: 9 pages, 5 figures
Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark--Ismail's two conjectures
Sharp inequalities for linear combinations of orthogonal martingales
Relations between $\mathcal{L}^p$- and Pointwise Convergence of Families of Functions Indexed by the Unit Interval
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