In order to estimate the average age, denoted by ????, of all eligible voters in Michigan Congressional District 14, three methods are used to form a point estimate

In order to estimate the average age, denoted by ????, of all eligible voters in Michigan Congressional District 14, three methods are used to form a point estimate. Method 1: randomly sample an eligible voter in the District and use his/her age as the point estimate, denoted by ????1. Method 2: randomly sample 10 eligible voters in the District. For each sampled voter ????, take his/her age as ???????? , then let the point estimate be ????2 = (????1 + ? + ????10)/10 Method 3: Use ????3 = (????1 + ????2)/2 as the point estimate (a) Which of the following statements are correct? A. Method 1 produces an unbiased estimator (call it Estimator 1) B. Method 2 produces an unbiased estimator (call it Estimator 2) C. Method 3 produces an unbiased estimator (call it Estimator 3) D. The probability distribution of Estimator 1 is normal E. The probability distribution of Estimator 2 is normal F. The variance of Estimator 2 is smaller than the variance of Estimator 1 G. The variance of Estimator 3 is smaller than the variance of Estimator 2 H. If we repeat Method 1 ???? times and take the average of the point estimates ????1 thus obtained, i.e., ?????= (????1 + ????2 + ? + ????????)/????, this average ?????will be more and more close to ???? as we increase