Task 5 - Joint Densities [15 pts] Suppose that X, Y are jointly continuous rv's with joint density 4ry Or1,0sys1 fx,x (x, y) = otherwise (Observe that this is a probability density function since it is non-negative and " fx,y(zy) dydr = Ary dy da = (2xu |" ) dx - |2xdx = = 1.) Your answers below should not be evaluated unless otherwise specified. Your answers should usually be in terms of integrals or double integrals. a) Write an expression which we can evaluate to find P(Y > X). Hint: draw the region of the joint density, and the desired region. b) Write an expression which we can evaluate to find the marginal density fx (x). Specify the value of fx (x) for all r e R. Do the same for fy (y). c) Are X and Y independent? Justify your answer. (You may need to evaluate an integral or two to do this.)