Question: f3. (5 points) Suppose we draw n random samples (X1, . .., Xn), and an estimator O(X1, . .. , Xn) is proposed as O


\f3. (5 points) Suppose we draw n random samples (X1, . .., Xn), and an estimator O(X1, . .. , Xn) is proposed as O (X1 , . . . , Xn) = 1 - n Exil(X; #0, and Xi # 6), i=1 where I(.) is an indicator function, I(X; # 0, and X; # 6) =0, if X; 6 {0, 6}, and I(X; # 0, and X; # 6) = 1, if X; 6 {2, 4}. More specifically, we only take the summation for all samples NOT equal to 0 or 6. Is O(X], . .., X,) a an unbiased estimator for E(X). Why? (Hint: find probability mass function of XI(X / 0, and X # 6).)
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