3.18 .

(a) Show that the dispersion variance ????(0|V) as defined in Eq. (3.60) continues to make sense for an intrinsic random field with semivariogram

????(h), and is given in this case by

????(0|V) = |V|

−2

∫ ∫ ????(s − t) ds dt.

To verify this formula, it is helpful to expand (3.60) as

????(0|V) = |V|

−3

∫V ∫V ∫V E{[X(t) − X(s)][X(t) − X(u)]} ds du dt, and to use (3.3) to simplify the result.

(b) If ????(h) = |h|

2???? for some 0 0, show that

????(0|????V) = B????2????, B = |V|

−2

∫V ∫V

|s − t|

2???? ds dt, and

????(????1V|????2V)=(????2????

2 − ????2????

1 )B > 0 for 0 < ????1 < ????2