14 further the marginal pdfs are f x x 1 6 xy 2 dy 2

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14
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Further, the marginal PDFs are f X x 0 1 6 xy 2 dy 2 x 0 1 3 y 2 dy 2 x f Y y 0 1 6 xy 2 dx 3 y 2 0 1 2 xdx 3 y 2 15
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Computing joint probabilities is done by integrating the joint distribution over the appropriate region. Suppose we want P X Y 1 . The event of interest is A  x , y : x y 1,0 x 1,0 y 1  x , y : 0 x 1 y ,0 y 1 and so we integrate the joint density over this region: 16
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P X Y 1 0 1 0 1 y 6 xy 2 dxdy 0 1 0 1 y 2 xdx 3 y 2 dy 0 1 3 1 y 2 y 2 dy 3 0 1 y 2 2 y 3 y 4 3 1 3 2 4 1 5 1 10 17
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