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

question 1

Multiple Choice

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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