If X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p), what is the variance of the sample mean Xˉ=Xn\bar{X} = \frac{X}{n}Xˉ=nX?
p(1−p)n\frac{p(1-p)}{n}np(1−p)
np(1−p)np(1-p)np(1−p)
n2p(1−p)n^2p(1-p)n2p(1−p)
p(1−p)p(1-p)p(1−p)