If fX(x) is the density function of X 1

,…,X p, show that the density of Y

r = a r + a r

iXi is fY (y) = JfX {b i

r (y r − a r)}, where b i

ra r

j = δ

i j and J is the determinant of b i

r

. Hence show that the partial derivatives of log fX(x) are Cartesian tensors.