Given n independent binary variables X,,X,...,X,, that can take the values of 0 or 1, are identically distributed as X, - Ber(0) where i – 1,2,...,n. Consider the estimator Ô = -x, . (i) Describe the distribution of the random variable S – nð . (ii) Identify the mean and variance of this distribution. (iii) By writing ô in terms of S, compute the expectation E(Ö) and the bias of this estimator. State whether this estimator unbiased. (iv) Based on distribution of nð , examine vai(0) and the standaid enoi of this estimator.

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