3. Cubic correlation function The cubic correlation function is given by R(xi x j|) = d k=1 R(xik x jk |) where

3. Cubic correlation function The cubic correlation function is given by R(xi − x j|ξ) =  d k=1 R(xik − x jk |ξ) where R(xik − x jk |ξ) = ⎧ ⎪⎪⎪⎨ ⎪⎪⎪⎩ 1 − 6  xik−x jk θk 2 + 6 |xik−x jk | θk 3 if |xik − x jk | ≤ θk 2 2  1 − |xik−x jk | θk 3  if θk 2 < |xik − x jk | ≤ θk 0 if θk < |xik − x jk | , where ξ represents the parameters (θ1, θ2 ..., θd ), and θk > 0. Repeat Exercise 1 with the cubic correlation function and d = 1.