Question: If 1 = X/n , 2 = X + 1 / n+ 2 , and 3 = 1/3 are estimators of the parameter of

If Θ1 = X/n , Θ2 = X + 1 / n+ 2 , and Θ3 = 1/3 are estimators of the parameter θ of a binomial population and θ = 1/2 , for what values of n is
(a) The mean square error of Θ2 less than the variance of Θ1;
(b) The mean square error of Θ3 less than the variance of Θ1?

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