By considering the expression var {i,jXiXj ciXi} with ci = i,rs,t r,s,t , show that 4

By considering the expression var {κi,jXiXj − ciXi}

with ci = κi,rκs,tκ

r,s,t

, show that ρ4 ≥ ρ

2 13 − 2, where 4 and ρ

2 13 are defined by (2.14)

and (2.16). In addition, by examining the expression

∫ (a + aix i + aijx ix j)

2 fX (x)dx, show that ρ4 = ρ

2 13 − 2 if and only if the joint distribution of X is concentrated on a particular class of conic.