Sum of I.I.D Random Variables

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Expected number of variables required to surpass 1

This research investigates uniform convergence properties in infinite series and their applications in various mathematical contexts, particularly analyzing sums of uniform random variables.

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Abstract

This paper explores the properties of sums of uniform random variables and the convergence behavior of associated infinite series. We analyze the theoretical foundations of uniform convergence and demonstrate practical applications in probability theory and statistical analysis. The results provide insights into limit distributions and convergence rates for sums of independent uniform random variables.