The Gauss-Markov Theorem Proves That A $t$ Distributed $X _ { 1 } , \ldots , X _ { n }$

Short Answer

The Gauss-Markov Theorem proves that a. the OLS estimator is $t$ distributed.
b. the OLS estimator has the smallest mean square error.
c. the OLS estimator is unbiased.
d. with homoskedastic errors, the OLS estimator has the smallest variance in the class of linear and unbiased estimators, conditional on $X _ { 1 } , \ldots , X _ { n }$ .