Let the statistic U2 be as defined by Eq. (11.3.32), and let be fixed positive constant.

Let the statistic U2 be as defined by Eq. (11.3.32), and let γ be fixed positive constant. Show that for all observed values (xi , yi), for i = 1, . . . , n, the set of points (β∗0, β∗1) such that U2 < γ is the interior of an ellipse in the β∗0β∗1 - plane.