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Suppose that X and Y are random variables such that (X,

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Suppose that X and Y are random variables such that (X, Y ) must belong to the rectangle in the xy-plane containing all

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Suppose that X and Y are random variables such that (X, Y ) must belong to the rectangle in the xy-plane containing all points (x, y) for which 0 ? x ? 3 and 0 ? y ? 4. Suppose also that the joint c.d.f. of X and Y at every point (x, y) in this rectangle is specified as follows: F (x, y) = 1 156xy(x2 + y). Determine (a) Pr(1 ? X ? 2 and 1 ? Y ? 2); (b) Pr(2 ? X ? 4 and 2 ? Y ? 4); (c) the c.d.f. of Y ; (d) the joint p.d.f. of X and Y ; (e) Pr(Y ? X).

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