True/False. Please read the statements carefully, as no partial credit will be given. (a) If ?? is a strong consistent estimator of ?, then e ?? a.s ?? e ? . (b) The maximum likelihood estimator (MLE) based on a random sample of independent and identically distributed random variables, X1, , Xn, is always same as the MLE based on their order statistics. (c) All unbiased estimators are consistent. (d) Under the regularity conditions, an maximum likelihood estimator is consistent, and its variance is same as the inverse of the Fisher information. (e) All maximum likelihood estimators are efficient. (f) An efficient estimator is always unbiased.

3 points) True False. Please read the statements carefully, as no partial credit will be given. (a) If d is a strong consistent estimator of 0, then eyes. (b) The maximum likelihood estimator (MLE) based on a random sample of independent and identically distributed random variables, X1, . . . , Xn, is always same as the MLE based on their order statistics. (c) All unbiased estimators are consistent. (d) Under the regularity conditions, an maximum likelihood estimator is con- sistent, and its variance is same as the inverse of the Fisher information. (e) All maximum likelihood estimators are efficient. ( f ) An efficient estimator is always unbiased