Let $X_1,\ldots,X_n$ be a random sample of Pois$(1)$. Then: $$P\left(F\left(\bar X_n\right)<F(1)\right) = P\left(\bar X_n<1\right) \to 1/2$$ as $n \to \infty$. Is this true and if so, why or why not?
2026-03-26 03:09:27.1774494567
Probability Poisson sample mean convergency
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