54. If X and Y have joint density function $$ f(x, y) = frac{1}{xy} $$ x ...

54. If X and Y have joint density function

$$

f(x, y) = \frac{1}{x²y²}

$$

x ≥ 1, y ≥ 1

(a) Compute the joint density function of U = XY, V = X/Y.

(b) What are the marginal densities?