A simple procedure for deriving the probability density function (pdf) for sums of uniformly distributed random variables is offered. This method is suited to introductory courses in probability and ...

Suppose a1, a2,... is a sequence of real numbers with an → ∞. If $\lim \sup(X_1 + \cdots + X_n)/a_n = \alpha$ a.s. for every sequence of independent nonnegative uniformly bounded random variables X1, ...