Suppose X and Y have joint density f (x, y). Are X and Y independent if (a)
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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) = 6xy2 when x, y ≥ 0 and x + y ≤ 1?
(c) F (x, y) = 2xy + x 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? In each case, f (x, y) = 0 otherwise.
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