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

Info icon This preview shows pages 14–24. Sign up to view the full content.

View Full Document Right Arrow Icon
14
Image of page 14

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 15
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
Image of page 16

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 17