Can anyone help me with it:
Using the central limit theorem for suitable Poisson random variables, prove that $$ \lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}=1/2$$
Thanks!
Answer
Hint: A Poisson$(n)$ random variable can be represented as the sum of $n$ i.i.d. Poisson$(1)$ rv's.
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