- #1
Chris L T521
Gold Member
MHB
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Thanks to those who participated in last week's POTW! Here's this week's problem!
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Problem: Show that $\displaystyle\lim_{n\to\infty}e^{-n}\sum_{k=0}^n \frac{n^k}{k!}=\frac{1}{2}$.
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Hint:
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Problem: Show that $\displaystyle\lim_{n\to\infty}e^{-n}\sum_{k=0}^n \frac{n^k}{k!}=\frac{1}{2}$.
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Hint:
Let $X_n$ be a Poisson random variable with mean $n$. Use the Central Limit Theorem to show that $\mathbb{P}\{X_n\leq n\}\rightarrow \frac{1}{2}$.