Let β̂_M= log (p₊₁p₂₊/p₊₂p₁₊) refer to marginal model (10.6) and β̂_C= log (n₂₁/n₁₂) to conditional model (10.8). Using the delta method, show that the asymptotic variance of ˆšn(β̂_M€“ β_M) is

(Ï€₁₊ Ï€₂₊)^€“1 + (Ï€₊₁ Ï€₊₂)^€“1 €“ 2(Ï€₁₁ Ï€₂₂ €“ Ï€₁₂ Ï€₂₁)/(Ï€₁₊ Ï€₂₊ Ï€₊₁ Ï€₊₂).

Under the independence condition of the previous problem, β_M = β_C. In that case, show that the asymptotic variances satisfy

var n (BM )] -(, ) + (, , ) < (, )+ (.1 +)7!. - + - ar ( ] %3D