3.2 Verify the formula var {∑n i=1 ai XI(ti

)

}

= −∑n i,j=1 ai aj

????(ti − tj

)

for an intrinsic random field {XI(t)} of order 0 with semivariogram ????(h), where a(n × 1) is an increment vector of order 0, i.e. ∑ ai = 0.

Hint: Write ∑ ai XI(ti

) = ∑ ai

[XI(ti

) − XI(t0)] for any other site t0, and using

(3.3) show that var {∑ai XI(ti

)

}

= var {∑ai

[XI(ti

) − XI(t0)]}

= ∑

i,j ai aj cov{[XI(ti

) − XI(t0)], [XI(tj

) − XI(t0)]}

= ∑ai aj

{????(ti − t0) + ????(tj − t0) − ????(0) − ????(ti − tj

)}

= −∑ai aj

{????(ti − tj

)}.