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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Elementary Probability For Applications

ISBN: 9780521867566

1st Edition

Authors: Rick Durrett

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Question Posted: Jan 12, 2024 04:00 AM

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Suppose X and Y have joint density f (x, y). Are X and Y independent if (a)

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Elementary Probability For Applications

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