3. Let fxy(x,y) be the joint probability function of two random variables X and Y. Suppose that the joint moment generating function is M_(X,Y)(t_1, t_2) = E(e^t_1 X + t_2 Y) = [ 1/3(e^t_1 + t_2 + 1) + 1/6(e^t_1 + e^t_2) ]^2 (a) (5%) Find the joint probability function of X and Y.

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 \(K_{2}\)

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