Let 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→∞?
Normal(0,1)\text{Normal}(0, 1)Normal(0,1)
Poisson(np)\text{Poisson}(np)Poisson(np)
Uniform(0,1)\text{Uniform}(0, 1)Uniform(0,1)
Exponential(1)\text{Exponential}(1)Exponential(1)