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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Uniformly bounded sequence {X_i} of independent random variables series converges or diverge...
Let $\{X_i\}$ be a uniformly bounded sequence of independent random variables. Does $\sum_{i=1}^{\infty}X_i-E[X_i]$ converges or diverges, depending on whether $\sum_{i=1}^{\infty}\sigma_i^{2}$ conver …