Consider the Model Y_i = β₁X_i + U_i, Where U_i $x _ { i } ^ { 2 }$

Essay

Consider the model Y_i = β₁X_i + u_i, where u_i = c $x _ { i } ^ { 2 }$ e_i and all of the X's and e's are i.i.d. and distributed N(0,1).
(a)Which of the Extended Least Squares Assumptions are satisfied here? Prove your assertions.
(b)Would an OLS estimator of β₁ be efficient here?
(c)How would you estimate β₁ by WLS?