1. For locations s; and s, and random variables associated with Z(s;) and Z (s; ) the variogram is defined as 2y(s; - s,) = var Z(s;) - Z(s;)}; Vsi, s; ED (3) Show that any function 2y(s; - s; ) that satisfies (3) must satisfy the required property of a variogram; that is, the property of being conditionally definite negative. Hint: For the requested proof, make use of the following two algebraic identities: Identity 1: for any real numbers {W{ : i = 1, ..., m} and {a; : i = 1, ..., m}, m 2 m m [aw.) = [Eqq, w.W; i=1 i=1 j=1 Identity 2: for any real numbers {W; : i = 1, ..., m} and {a; : i = 1, ..., m}, such that 2i-1a; = 0, m 2 m m a; Wi 1 2 a;a; (Wi - W, ) 2 i=1 i=1 j=1