In the Case When the Errors Are Homoskedastic and Normally $\hat \beta$

In the case when the errors are homoskedastic and normally distributed, conditional on X, then

A) $\hat \beta$ is distributed N(?, $\sum _ { \hat { \beta } \mid X }$ ) ,where $\sum _ { \hat { \beta } \mid X }$ = $\sigma _ { u } ^ { 2 }$ I_(k+1) .
B) $\hat \beta$ is distributed N(?, $\sum _ { \hat { \beta } }$ ) , where $\sum _ { \hat { \beta } }$ = $\sum _ { \sqrt { n } \left( \hat { \boldsymbol { \beta } } _ { - } \boldsymbol { \beta } \right) }$ /n = $Q _ { X } ^ { - 1 }$ $\sum _ { V }$ $Q _ { X } ^ { - 1 }$ /n.
C) $\hat \beta$ is distributed N(?, $\sum _ { \hat { \beta } \mid X }$ ) ,where $\sum _ { \hat { \beta } \mid X }$ = $\sigma _ { u } ^ { 2 }$ ( $X ^ { \prime }$ X) ^-1.
D) $\hat { u }$ = P_XY where P_X = X( $X ^ { \prime }$ X) ^-1 $X ^ { \prime }$

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