For any which is an interior point of the natural parameter space, the expectations and covariances

For any θ which is an interior point of the natural parameter space, the expectations and covariances of the statistics Tj in the exponential family (2.35) are given by E [Tj (X)] = −∂ log C(θ)

∂θj

(j = 1,...,k), E [Ti(X)Tj (X)] − [ETi(X)ETj (X)] = −∂2 log C(θ)

∂θi∂θj

(i, j = 1,...,k).