In maximizing the likelihood (12.2.13), we first minimized, for each value of α, β, and Ï2δ, the function with respect to ξ1,..., ξn. (a) Prove

In maximizing the likelihood (12.2.13), we first minimized, for each value of α, β, and σ2δ, the function

with respect to ξ1,..., ξn.
(a) Prove that this function is minimized at

(b) Show that the function

defines a metric between the points (x, y) and (ξ, a + βξ) A metric is a distance measure, a function D that measures the distance between two points A and B. A metric satisfies the following four properties:
i. D(A, A) = 0.
ii. D(A, B) > 0 if A ‰  B.
iii. D(A, B) = D(B, A) (reflexive).
iv. D(A, B) ‰¤ D(A, C) + D(C, B) (triangle inequality).

S(61....6n) = (i - 6) + A( - (a +BEJ))*) i=1