(b) Assume that n independent count variables {X,X,...,X,} are identically distributed as X, ~ Poi(0) where i=1,2,...,n and to estimate E(X;)=0 , consider the sample mean estimator ê = -X,. (i) Describe the distribution of the random variable S=nô. Use the expectation of the distribution of S = nỗ to compute the expectation E(Ô) and the bias of this estimator. State whether this estimator unbiased. (ii) (iii) Use the variance of the distribution of S=nô to examine var(@) and the standard error of this estimator. Use the variance and the bias of ê to compute the Mean Squaled Eifor (MSE) of this estimator. Comment on the MSE behaviour in the asymptotic limit as n → n. State whether this estimator is consistent or not (iv)

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