Poisson Distribution Approximated by Normal Distribution

Theorem

Let $X$ be a discrete random variable which has the Poisson distribution $\Poisson \lambda$.

Then for large $\lambda$:

$\Poisson \lambda \approx \Gaussian \lambda \lambda$

where $\Gaussian \lambda \lambda$ denotes the normal distribution.


Proof


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In particular: Use Central Limit Theorem
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Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): normal approximation
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