7. Let X1,X2, . . . ,Xn be iid RVs with E|X1|4 <∞. Let var(X) = σ2 and β2 = μ4/σ4:

(a) Show, using the CLT for iid RVs, that

√

n(S2−σ2)

−L→N(0,μ4−σ4).

(b) Find a transformation g such that g(S2) has an asymptotic distribution which depends on β2 alone but not on σ2.