8.4 Suppose the signal S in Exercise 8.2 comes from a stationary Gaussian process with mean ???? and covariance function ????(h), observed at sites t1, ..., tn, with ????(0) = ????2. Show that the elements of the observation vector Z have a constant mean and covariances, which can be expressed in terms of a new covariance function ????(h) and a nugget effect as cov(Zi

, Zj

) = c1????(ti − tj

) + c2I[i = j], where ????(h) = exp(????(h)) − 1 and where the indicator function I[i = j] is 1 if i = j and 0 otherwise. What are the values of c1 and c2? What happens if ????2 is small so that exp(????(h)) − 1 ≈ ????(h) for all h?