Which of the following four statistics is the best estimator

Which of the following four statistics is the best estimator of the parameter = 4 and why? (you should provide TWO reasons)

Statistic A has a mean of 4 and a standard deviation of 14
Statistic B has a mean of 4 and a standard deviation of 16
Statistic C has a mean of 3 and a standard deviation of 14
Statistic D has a mean of 5 and a standard deviation of 12

now I would think it is either Statistic A since the mean of 4 is equal to the parameter of 4 or Statistic D because that has the smallest spread. I can\'t think of another reason though.

Solution

Option A is correct becuase mean of statistics A is equal to paremeter theta and also standard devaition is small than B.