Suppose x and y have joint density fxy are x and y

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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

(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).

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