Show that the array M ij () = E {XiXj exp (rx r)} is positive definite for each . Hence deduce that the function ()

Show that the array M ij (ξ) = E {XiXj exp (ξrx r)}

is positive definite for each ξ. Hence deduce that the function Μ(ξ) is convex.

Under what conditions is the inequality strict?