-) Suppose X and Y are continuous random variables. The range of X is [1,3], the range of Y is [0, 1]. The joint pdf of X and Y be given by f(x, y) = 2xy³ - 2y³. Verify if X and Y independent random variables.

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Let random variables X and Y have the joint pdf   fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1   0, otherwise   Find the joint pdf of U = X^2 and V = XY.

We have a random variable X and Y that jave the joint pdf f(x) = {1    0<x<1, 0<y<1}                                                                                                                                                          {0         otherwise} Let U = Y - X2.  What is the support for the random variable U? Are there critical points? If  U = Y/X.       What is the support for the random variable U? Are there critical points?