Consider X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). What is the limiting distribution of Y=X−npnp(1−p)Y = \frac{X - np}{\sqrt{np(1-p)}}Y=np(1−p)X−np as n→∞n \to \inftyn→∞?
Standard Normal N(0,1)N(0, 1)N(0,1)
Poisson
Cauchy
Uniform