題組內容

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 $$M_{(X,Y)}(t_1, t_2) = E(e^{t_1 X + t_2 Y}) = \left[ \frac{1}{3}(e^{t_1 + t_2} + 1) + \frac{1}{6}(e^{t_1} + e^{t_2}) \right]^2$$

(a) \( (5\%) \) Find the joint probability function of X and Y.