題組內容

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

(3) Find the conditional probability density functions of \( f(x|Y=2) \) and \( f(y|X=1) \). (10%)