Conditonal Density Function

Question

$$f_{X,Y}(x,y)= \begin{cases} (x-y) & 0 \lt x \lt 1, & -1 \lt y \lt 0 \\ 0 & \text{elsewhere} \end{cases}$$

How can I find the conditional density function $Y$ $$f_Y(y | X \le0)$$

Answer 1

The conditional density for $f_Y$ conditioned on $X < 0$ is not well defined because the event $X<0$ can never happen.