Taking the definition of Y* as given in the previous exercise, show that W/2 = (Y

∗)

2 = X2/2 − ρ3X3/3! − {ρ4 − 3ρ

2 3}X4/4!

has mean given by E (W) = 1 + (5ρ

2 3 − 3ρ4)/12 = 1 + b/n.

Deduce that W

1+b/n

~χ

2 1 + O (n

−3/2).