Which estimator is better?
Suppose that n=5 observations are taken from the uniform pdf, f_Y(y;theta)=1/theta, 0<=y<=theta, where theta is unknown. Two unbiased estimators for theta are theta hat_1 = (6/5)*Y_max and
theta hat_2 = 6*Y_min. Which estimator would be better to use? Does the answer as to which estimator is better make sense on intuitive grounds? Explain.
Hint: What must be true of Var(Y_max) and Var(Y_min) given that f_Y(y;theta) is symmetric? Note that Var(Y_max) and Var(Y_min) do not need to be formally calculated.