題組內容

3. Two random variables X and Y have a joint probability density function of the form \[ f_{XY}(x, y) = \begin{cases} a(2x + y - xy), & 0 \le x \le 1, 0 \le y \le 2, \\ 0, & elsewhere. \end{cases} \]

(2)Find the marginal probability density functions of \( f_X(x) \) and \( f_Y(y) \). (10%)