Suppose X and Y have joint density f(x,y). Are X and Y independent if:
(a) f(x,y) = xe^-x(1+y) for x,y >= 0
(b) f(x,y) = 6xy^2 when x,y >= 0 and x+y <= 1
(c) f(x,y) = 2xy + when 0 < x < 1 and 0 < y < 1
(d) f(x,y) = (x+y)^2 - (x-y)^2 when 0 < x < 1 and 0 < y < 1
*If domain is not rectangular, then f(x,y) does not equal f(x)*f(y).
Show domains and calculations for f(x) and f(y).