Let X1,X2,…,Xn∼Bernoulli(p)X_1, X_2, \ldots, X_n \sim \text{Bernoulli}(p)X1,X2,…,Xn∼Bernoulli(p) be i.i.d. What is the variance of p^=1n∑Xi\hat{p} = \frac{1}{n}\sum X_ip^=n1∑Xi?
p(1−p)p(1-p)p(1−p)
p(1−p)n\frac{p(1-p)}{n}np(1−p)
p2(1−p)2p^2(1-p)^2p2(1−p)2
np(1−p)np(1-p)np(1−p)