題組內容

3. Let Xi = (Xi1, Xi2)', i = 1, ..., n, be i.i.d. bivariate normal with unknown (μ1, μ2)' = E[X1] and Var(X1). Let θ = μ2/μ1 be the parameter of interest (μ1 ≠ 0). Define Yi(θ) = Xi2 - θXi1.

(c) \( (5\%) \) Use the pivotal quantity of (b) to find a \( 100(1 - \alpha)\% \) confidence set, \( C(X) \), for \( \theta \).