Let Xn∼Poisson(n)X_n \sim \text{Poisson}(n)Xn∼Poisson(n). Find the limit as n→∞n \to \inftyn→∞ of the expected value E[∣Xn−nn∣]E\left[\left| \frac{X_n - n}{\sqrt{n}} \right|\right]E[nXn−n].
2π\sqrt{\frac{2}{\pi}}π2
111
12π\frac{1}{\sqrt{2\pi}}2π1
π\sqrt{\pi}π