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 geometrical considerations in multidimensional Euclidean spaces, we find the function which expresses the expected value. Especially, in the case of two pointed a priory given sequence, we will find close form function for the expected values.
For all a priory numbers equal 1, it reduces to problem solved by B. \'Curgus and R.I. Jewetts in 2007. and solution to the exponential function.

{\bf AMS Subj. Class.}: 34K60, 60G50, 33B10.

{\bf Keywords:} $n$--dimensional geometry, experiment, expected value.

%33B10 Exponential and trigonometric functions
% 34K60 Qualitative investigation and simulation of models
% 60G50 Sums of independent random variables; random walks
%30B50 Dirichlet series and other series expansions, exponential series

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\begin{thebibliography}{99}

\bibitem{Curgus}
        B. \'Curgus, R.I. Jewett, {\it An unexpected limit of expected values},  Expo. Math.  {\bf 25} (2007) 1--20.

\bibitem{Rajkovic}
        P.M. Rajkovi\'c, S.D. Marinkovi\'c, M.S. Stankovi\'c,
             {\it Power series determined by an expreminet on the unit interval},
             arXiv:1304.2790v1 [math.CA] 8 Apr 2013

\end{thebibliography}