..., Problem 3. Let X,. Xn be a random sample from a population with pdf =...

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..., Problem 3. Let X,. Xn be a random sample from a population with pdf = f(x;0). In each of the three cases below, confirm that the given function is indeed a pdf, compute the MSE of the given estimator On of 0, and check whether the MSE goes to zero as n o: Case 1 f (x; 0) = a 1; -a axa- -a-1 " a>0,0 < x < 0; n = X(n) = max(X1,...,. Xn); Case 2: f(x; 0) = ax, a > 0, 0 < 0 < x; = n = X(1) = min(X, , Xn); Case 3: f(x; 0) = 0ex/0, x > 0, 0 > 0; n = nX(1). ..., Problem 3. Let X,. Xn be a random sample from a population with pdf = f(x;0). In each of the three cases below, confirm that the given function is indeed a pdf, compute the MSE of the given estimator On of 0, and check whether the MSE goes to zero as n o: Case 1 f (x; 0) = a 1; -a axa- -a-1 " a>0,0 < x < 0; n = X(n) = max(X1,...,. Xn); Case 2: f(x; 0) = ax, a > 0, 0 < 0 < x; = n = X(1) = min(X, , Xn); Case 3: f(x; 0) = 0ex/0, x > 0, 0 > 0; n = nX(1).