(ii) If $x_{i}$ follows Bernoulli $(p)$, show that $$ \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}=\bar{x}(1- \bar{x}) $$ so that the unbiased estimator of $\operatorname{Var}(\bar{x})$ is $$ \frac{1}{n} s^{2}=\frac{1}{n}\left(\frac{1}{n-1} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}\right)=\frac{\bar{x}(1- \bar{x})}{n-1} . $$ SP. JG.079

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