A pair of random variablesxy is equally likely to fall

Question

Consider again the random variables in given exercise that are uniformly distributed over an ellipse..

Exercise

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, and ƒ_X(x) f_Y(y)

(c) Find and Pr(X > 1) Pr(Y 1)

(d) Find Pr(Y 1 X > 1) . Are the events {X > 1}  and  {Y 1}independent?