The following random variables X and Y follow a joint probability density function:
$$f(x,y)=\begin{cases}kxy & \text{for 2 < x < 4 and 2 < y < 7 - x } & \\ 0 \ \ \ \ \ \ \ \ \ \text{otherwise}\end{cases}$$
I understand there are two methods in finding k,
However, I am confused as to why fixing Y first will not result in the probability being 1. Could the reason be because of how I calculated my upper and lower boundaries for x and y?
I would be very grateful to receive any constructive feedback regarding my question. Thank you!
Hint: Fixing $Y$ will divide the whole integral in 2 parts-when $0<Y<3$ then $2<X<4$ and when $3<Y<5$ then $2<X<7-Y$