Let \(y \sim \operatorname{Poisson}(\mu)\).

(a) If \(\mu=n\) is an integer, show that the normalized variable \(\frac{y-\mu}{\sqrt{\mu}}\) has an asymptotic normal distribution \(N(0,1)\), i.e., \(\frac{y-\mu}{\sqrt{\mu}} \sim_{a} N(0,1)\) as \(\mu\rightarrow \infty\).

(b) Generalize the conclusion in

(a) to an arbitrary constant \(\mu\).