題組內容

5. Consider \( Y = \beta_0 + \beta_1 X + \varepsilon \) with \( E(\varepsilon) = 0 \), \( \text{Var}(\varepsilon) = \sigma^2 \) and \( \varepsilon \) are uncorrelated.

(a) Show that cov(\( \hat{\beta}_0, \hat{\beta}_1 \)) =? ( 5 分 )