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.

(a) \( (5\%) \) It is known that \( Y_{1}(\theta),\ldots ,Y_{n}(\theta) \) are i.i.d. with \( N(K_{1},K_{2}) \) . Find \( K_{1} \) and \( K_{2} \)