Equation (A7) leads straight away into the optimal value of ? * appearing in Equation (8).

Equation (A7) leads straight away into the optimal value of ? * appearing in Equation (8).

The presumption of analytical self-reliance shows that the joint likelihood thickness purpose of the elements of ?X? is:

(B1) f X; ? 1, ? 2, … ? m = ? i = 1 m ? i e — ? i = 1 m ? i x i (B1)

The likelihood that the arbitrary development will have attributes satisfying the conditions imposed by the minimal set is:

(B2) P r o b x 1 x 1, min, …. X n x n, min = 1 — F X min = e — ? i = 1 n ? i x i, min (B2)

The numerator for the expected energy in Equation (4) when you look at the special instance is:

(B3) ? x n, min ? ? ? x 1, min ? U X f X d x 1 ? d x n = ? x n, min ? ? ?