I am studying for actuarial Exam P using Finan's notes. I have come across a joint probability problem I do not understand how to solve and the answer key only adds to my confusion.
The problem is:
Let $X$ and $Y$ be continuous random variables, with the joint probability density function
$$ f_{XY}(x,y)=\frac{3x^2+2y}{24} $$ for $ 0\le x, y\le 2$ and $0$ otherwise. Find $ f_X(x)$ and $f_Y(y)$.
The answer key has the bounds of integration for both integrals to be 0 to 2 and I do not understand why as this does not seem to cover the range of the variables. For example, is $(50, 1)$ not a valid input into $f_{XY}(x,y)$? Any help is greatly appreciated!