題組內容

2. Let $X$ and $Y$ be random variables with joint density function

$$f(x, y) = \begin{cases} 2, & x \ge 0, y \ge 0, 0 \le x + y \le 1 \\ 0, & \text{otherwise} \end{cases}$$

(b) \( (7\%) \) Find \( f_{X / Y}(x|Y = \frac{1}{2}) \), the conditional density of \( X \) given \( Y = \frac{1}{2} \).