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Let X and Y have joint density f(x, y) = 6/7(x + y)^2 if 0 ≤...

Let X and Y have joint density f(x, y) = 6/7(x + y)^2 if 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 otherwise, where c is a positive constant.

Compute the marginal densities of X and of Y (be explicit about all cases!).

Compute P(Y + 2X < 1).

Determine whether X and Y are independent. Justify your answer.

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