Question: A pair of random variables,(X , Y) , is equally likely to fall anywhere in the ellipse described by 9X2 + 4 Y2 < 36.

A pair of random variables,(X , Y) , is equally likely to fall anywhere in the ellipse described by 9X2 + 4 Y2 < 36.
(a) Write the form of the joint PDF, fX,Y (x, y).
(b) Find the marginal PDFs, fX (x) and FY (y).
(c) Find Pr (X > 1) and Pr (Y < 1)
(d) Find Pr (Y < 1 | X >1). Are the events {X > 1} and {Y < 1}independent?

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