By applying the second-order conditions for optimization (i.e., second-derivative test), show that the ML estimators of β 1 , β 2 , and Ï 2

By applying the second-order conditions for optimization (i.e., second-derivative test), show that the ML estimators of β₁, β₂, and σ²obtained by solving Eqs. (9), (10), and (11) do in fact maximize the likelihood function in Eq. (4).

Eq (9)

Eq (10)

Eq (11)

Eq (4)

-h- hX) =0 2 ( -h-hx)