Grinstead-Snell-Probability · Problem 9.2.15

Central Limit Theorem

Mathematics · central-limit-theorem-discrete-independent-trials

Problem

Find a sequence of uniformly bounded discrete independent random variables

\{X_n\}

such that the variance of their sum does not tend to

\infty

n \to \infty

, and such that their sum is not asymptotically normally distributed.