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A discrete distribution defined on the non-negative integers that has the property that the mean is equal to the variance.

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Convergence of poisson distribution

Let $X\sim \operatorname{Pois}(\lambda)$ and $x_1,\ldots,x_n$ observations following this distribution. I want to derive the analytical solution of the following series: $$\ell(\lambda):=\lim_{x\right …
Anthony Hauser's user avatar