Let X₁, X₂, ..., Xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-1 for 0 < x < 1, and zero otherwise. Which statement is correct? (1) The approximate variance of the maximum likelihood estimator of a is. (II) The approximate variance of the maximum likelihood estimator of a is (III) The approximate variance of the maximum likelihood estimator of a is α √n (IV) None of the above. Hint: The approximate variance of the maximum likelihood estimator of a parameter is , where I (0) is the Fisher information which is defined by nI(0) I(0) O (II) (IV) O (III) O (1) -E ² log f(X;0) 2020

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