Marginal distribiution of X and Y

Question

"The joint density function of (X,Y) is given by: f(x,y)=2 for |x|<=0.5,|y|<=0.5 and xy>=0.Otherwise f(x,y) equals 0. Find the marginal distribitions of X and Y and check if they are independent. " I was thinking about something like this, $$fx(x)=\int_{0.5}^{0.5} 2\;\mathrm{dy}=2$$ but the proper answer is supposed to be one(for X and Y).

Answer 1

Hints:

$$f_X(x)=\int f_{X,Y}(x,y)dy\text{ and }f_Y(y)=\int f_{X,Y}(x,y)dx$$

If there is independence then $f_X(x)f_Y(y)$ serves as PDF of $(X,Y)$, so check if that is indeed the case here and draw conclusions.