Let X 1

,…,X n

be independent and identically distributed. By expressing X̅ as a linear form and the sample variance, s 2

as a quadratic form, show that cov(X̅, s 2

) =

κ3/n. Hence show that corr(X̅, s 2

) → ρ3/(2 + ρ4)

1/2 as n → ∞. Show also that cov(X̅

2

, s 2

) = κ4/n + 2κ1κ3/n and show that the limiting correlation is non-zero in general for non-normal variables.