When y ∼ N(0, ????????), in terms of elements kij from the concentration matrix K = ????−1

???? , show that the pdf f for y has the form log f(y) = constant − 1 2

∑

i kiiy2 i −

∑

i

∑

j kijyiyj, and the elements of K are natural parameters in the exponential family representation. Explain why yi and yj are conditionally independent, given the other elements of y, if kij = 0. (As in Section 7.2.7, one can construct a graphical representation. A Gaussian graphical model, also called a covariance selection model, portrays the conditionally independent pairs by the absence of an edge. See Dempster (1972) and Lauritzen (1996).)