State with reason or proof whether each of the following statements is true or false. A zero mark will be given if a reason or proof is not provided. a) The OLS estimator of an unrestricted linear regression model has a variance-covariance matrix that differs from its restricted counterpart by a negative semidefinite matrix. b) If an estimator is efficient then it is unbiased. c) If the sequence of random variables {Z} converges in distribution to a random variable Z, then {Z} converges in probability to Z. d) The existence of all moments of a sequence of random variables {Z} is required to prove that {Z} converges in quadratic mean to a constant b. e) If an estimator is consistent then it is unbiased. f) In a multiple linear regression model, the assumption of homoscedasticity is necessary for its OLS estimator to be unbiased. g) Ifx, 's are independent Bernoulli random variables with unknown parameter p, we write the probability mass function of each x, as: ; x = (0, 1), 0