full detailed answer in letter order please $3.($Stock and Watson #$10\mathrm{.}10)$ a$.$ In the fixed effects regression model, are the fixed entity effects, $\backslash$alpha $\_$i$,$ consistently estimated as n $->\backslash$infty with T fixed? $($Hint: Analyze the model with no X: : : Y$\_$i t$=\backslash$alpha $\_$i$+$u$\_$i t $)$ b$.$ If n is large $($s a y$,$ n$=2000)$ but T is small $($ say, T$=4).$ do you think that the estimated values of $\backslash$alpha $\_$i are approximately normally distributed? Why or why not? $($Hint: Analyze the model $.$Y$\_$i t$=\backslash$alpha $\_$i$+$u$\_$i t$)$